40 IS10 Abstracts

IP1 age and video restoration. I will present the framework Approximate Inference in Graphical Models: The and provide numerous examples showing state-of-the-art Fenchel Duality Perspective results. I will then briefly show how to extend this to image classification, deriving energies and optimization pro- Quite a number of problems involving inference from data, cedures that lead to learning non-parametric dictionaries whether visual data or otherwise, can be set as a prob- for sparse representations optimized for classification. I lem of finding the most likely setting of variables of a will conclude by showing results on the extension of this to joint distribution over locally interacting variables. These sensing and the learning of incoherent dictionaries. Models include stereopsis, figure-ground segmentation, model-to- derived from universal coding are presented as well. The image matching, super-resolution, and so forth. Inference work I present in this talk is the result of great collabo- over locally interacting variables can be naturally repre- rations with J. Mairal, F. Rodriguez, J. Martin-Duarte, I. sented by a graphical model, however exact inference over Ramirez, F. Lecumberry, F. Bach, M. Elad, J. Ponce, and general graphs is computationally unwieldy. In the context A. Zisserman. of approximate inference, I will describe a general scheme for message passing update rules based on the framework Guillermo Sapiro of Fenchel duality. Using the framework we derive all University of Minnesota past inference algorithms like the Belief Propagation sum- Dept Electrical & Computer Engineering product and max-product, the Tree-Re-Weighted (TRW) [email protected] model as well as new convergent algorithms for maximum- a-posteriori (MAP) and marginal estimation using ”convex free energies”. Joint work with Tamir Hazan. IP4 From Shape Matching to Shape Mechanics: Geom- Amnon Shashua etry and Dynamics The Hebrew University of Jerusalem, Israel [email protected] During the last decades, the study of shape spaces has been driven by the accelerated development of imaging techniques in biomedical engineering and the emergence of IP2 computational anatomy. Starting from the basic and hard Operator Splitting Techniques in Image Processing problems of shape comparison, shape matching and modeling shape populations, a fascinating landscape is appear- Recently, operator splitting methods have been success- ing involving infinite dimensional manifolds, Lie groups, fully applied to various image processing tasks like the de- Riemannian geometry, Hamiltonian systems and Statistics. noising and deblurring of images also in the presence of Its connection with many existing mathematical theories, non-additive noise, inpainting, sparse recovery problems sometimes outside the usual scope of the imaging commu- and multi-task learning. Splitting methods allow us to de- nity, and the growing need for effective tools in shape anal- compose the original problem into subproblems which are ysis, provide an exciting playground for inter-disciplinary easier to solve.The talk reviews and relates various of these research and collaborations. This talks will visit some optimization methods from the point of view of averaged hot spots in this landscape and some challenges driven by operators, Bregman proximal point methods and primal- anatomical growth modeling. dual Lagrangian approaches. Attention is also paid to mul- tistep methods. Then, various examples are presented how Alain Trouvé splitting algorithms can be successfully applied to image Ecole Normale Supérieure, France recovery problems. [email protected]

Gabriele Steidl Institute of Mathematics und Computer Science IP5 Universitaet Mannheim, Germany The Inverse Problem of Seismic Velocities [email protected] To reasonable approximation, the construction of structural images of the earth’s interior, using seismic reflec- IP3 tion data as input, boils down to an inverse problem for Data Don’t Lie: Image Processing Via Learned Ef- the wave equation. This inverse problem requires that the ficient Representations spatially varying wave velocity (a coefficient in the wave equation) be determined from samples of solutions near the In a large number of disciplines, image acquisition has ad- boundary of the space-time domain of propagation. The vanced much faster than image analysis. This permits to data-fitting techniques that have proven effective in other replace a number of pre-defined concepts by learned ones. science and engineering inverse problems encounter funda- In particular, we can learn efficient image representations. mental mathematical obstacles in application to this one. Among these, sparse representations have recently drawn In response, the seismic prospecting industry has devised a much attention from the signal processing and learning collection of methods to extract earth structure from data, communities. The basic underlying model consist of con- that appear at first glance to have little to do with data- sidering that natural images, or signals in general, admit a fitting. I will describe the seismic inverse problem and the sparse decomposition in some redundant dictionary. This qualities that make it resistant to data-fitting, as well as an means that we can find a linear combination of a few atoms underlying mathematical structure that encompasses both from the dictionary that lead to an efficient representation the data-fitting and industrial approaches. This structure of the original signal. Recent results have shown that learn- supports variational principles, more general than the data- ing (overcomplete) non-parametric dictionaries for image fitting or least squares principle, which in some cases have representations, instead of using off-the-shelf ones, sig- proven effective tools for velocity estimation. nificantly improves numerous image and video processing tasks. In this talk, I will first briefly present results on William Symes learning multiscale overcomplete dictionaries for color im- Rice University IS10 Abstracts 41

[email protected] [email protected]

Carlos Brito-Loeza IP6 Centre for Mathematical Imaging Techniques and Compressed Sensing in Astronomy Department of Mathematical Sciences, University of Liverpool The spatial infrared astronomical satellite Herschel, [email protected] launched on May 14 2009, is the first satellite which has a compressed sensing (CS) coder included in its on board software. We will present our motivations for using Com- CP1 pressed Sensing in this project. Then we will describe the Method of Micromirrors For Catadioptric Sensor practical implementation of our CS coder/decoder. We Design will show from simulations that CS enables to recover data with a spatial resolution enhanced up to 30% with similar We present a novel method for catadioptric sensor design sensitivity compared to the averaging technique proposed which consists of a micromirror array, asymmetric mirror by ESA, and we will present preliminary results relative and an orthographic camera. The micromirror method al- to the CS performances on real Herschel data. Finally lows construction of any desired projection which was not we will show how other problems in astronomy such in- possible with single-mirror systems. We use Frobenius In- terferometric image deconvolution or gammay ray image tegrability Theorem to write a system of quasilinear PDEs, reconstruction can be also handled differently using CS. whose numerical solution is the camera projection and numerically integrate the normal vector field to compute the Jean-Luc Starck mirror surface. Laboratoire AIM, CEA/DSM-CNRS-Universite Paris Diderot Emek Kose Can CEA Saclay, DAPNIA/SEDI-SAP, Service Loyola Marymount University d’Astrophysique [email protected] [email protected]

CP1 CP1 Topological Gradient for Image Restoration by Optimal Geometric Transformations of Compact Anisotropic Diffusion Manifolds Topological asymptotic analysis provides tools to detect A fundamental mathematical problem underlying the sub- edges and their orientation. The purpose of this work ject of matching and minimal morphing of images is the is to show the possibilities of anisotropic topological gra- problem of minimal distortion bending and morphing of dient in image restoration. Previous methods based on compact manifolds. We consider cost functionals that mea- the topological gradient used isotropic diffusion to restore sure distortion of geometry produced by a diffeomorphism the image. These methods are improved here by using between two compact n-manifolds. Our cost functionals anisotropic diffusion, a texture detector and differentiat- measure the distortion in volume or the first (metric) and ing between principal and secondary edges. Numerical re- the second (curvature) fundamental forms. We prove the sults are presented, including a comparison with Non-Local existence of the least distortion energy maps. Means method. Oksana Bihun Stanislas Larnier,Jérôme Fehrenbach Concordia College, Moorhead, MN Université Paul Sabatier [email protected] Institut de Mathématiques de Toulouse [email protected], [email protected] CP1 A Fourth Order Nonlinear Pde-Based Image Reg- istration Model and Its Fast Algorithm CP1 Robust Optical Flow for Modeling Dynamical Sys- We first propose a new variational registration model using tems full curvature regularization, leading to superior results, for both smooth and nonsmooth deformations, to competitors Classical optical flow techniques assume conservation of in- including approximate curvatures of Fischer and Moder- tensity and a smoothness of the flow field. If these assump- sitzki (2003), Henn and Witsch (2005). Due to its non- tions are dropped, such techniques can be used to compute linearity and high order, multigrid methods with standard apparent flows between time snapshots of data that does smoothers lead to non-convergence. We then propose a not come from images, even if these flows are turbulent and primal-dual fixed point method as a new smoother to en- divergent. We present a variational optical flow approach able fast convergence of a nonlinear multigrid. Various based on the continuity equation and total-variation div- numerical experiments will be reported. curl regularization for computing the flow fields between species densities generated from a two-species predator- Noppadol Chumchob prey model. Though the dynamics of the model system Centre for Mathematical Imaging Techniques and could be analyzed mathematically from the model itself, Department of Mathematical Sciences, University of using an optical flow approach allows to apply dynamics Liverpool analysis methods directly to measured data, even in the [email protected] absence of an apriorimodel.

Ke Chen Aaron B. Luttman University of Liverpool Clarkson University 42 IS10 Abstracts

Department of Mathematics and Wiener filters, but the computational complexity is [email protected] the same as filtered backprojection. Applications of this method include biomedical imaging under rigid-body pa- Erik Bollt, Ranil Basnayake, Sean Kramer tient motion and problems with motion described by linear Clarkson University shift-invariant partial differential equations, including ad- [email protected], [email protected], vection and diffusion. [email protected] Mark Butala, Farzad Kamalabadi University of Illinois at Urbana-Champaign CP1 [email protected], [email protected] The Image Editing Pde’s

Poisson image editing techniques involve the solution of a CP2 Poisson equation where the second member is a modified Computing Tomographic Projection Operators on gradient field. Application are numerous: adding, remov- Unstructured Meshes ing objects, fusing images, deblocking, local contrast adjus- tament, etc. In this communication we review the many For tomography problems on unstructured meshes, e.g., recently proposed variants, give their asymptotic isotropic those from limited angle tomography, it is desirable to com- version, and show how all of them can recieve a fast imple- pute algebraic solutions. Algebraic reconstruction tech- mentation. The asymptotic equations results will be shown niques require computation of discrete approximations of on several significant experiments. projection operators, traditionally a difficult task on unstructured meshes. We present a novel ray tracing algo- Ana B. Petro rithm for computing such operators on a recursive mesh Universitat de les Illes Balears data structure. We show that this method works in arbi- [email protected] trary dimension and discuss its scalability relative to the mesh diameter. We also present a straightforward parallel Jean-Michel Morel extension to our algorithm. ENS Cachan Russell J. Hewett [email protected] University of Illinois at Urbana-Champaign [email protected] Catalina Sbert Universitat de les Illes Balears William Cochran [email protected] Oak Ridge National Laboratory [email protected] CP1 The Minkowski Functionals: An Objective Tool to CP2 Quantify Typeface Legibility Time-Dependent Tomographic Imaging of the So- Text legibility is function of numerous elements such as the lar Atmosphere specific typeface (serif or sans serif), the character height Solar coronal tomography is concerned with reconstructing or the interletter spacing. The experiments assessing leg- the volumetric structure of the inner atmosphere of the Sun ibility have been greatly impacted by the choice of hu- based on a series of 2-D projection observations. We use man participants in the reading tests. We propose using a Monte Carlo approximation to the Kalman filter to es- Minkowski functionals, which are widely used to describe timate time dependent 3-D reconstructions that are more complex morphologies, to quantify the image of a text af- physically correct and significantly more efficient to com- ter erosion and dilatation. We bring out the role played by pute than those from classical time-invariant techniques. serifs. Empirical reconstructions of the coronal electron density Jean F. Poiraudeau distribution from this algorithm will be presented. IUT, Limoges University Farzad Kamalabadi, Russell J. Hewett, Mark Butala [email protected] University of Illinois at Urbana-Champaign [email protected], [email protected], Isabelle Blasquez [email protected] Limoges University [email protected] CP2 Pierre fournier Resistor Networks and Optimal Grids for the Elec- LICN-IUT du Limousin trical Impedance Tomography with Partial Bound- [email protected] ary Measurements.

Electrical impedance tomography with partial boundary CP2 measurements is a problem of ﬁnding the electrical con- Optimal Dynamic Tomography for Wide-Sense ductivity inside a domain from simultaneous measurements Stationary Spatial Random Fields of voltages and currents on a part of its boundary. Even in the case of full boundary measurements the problem We present a new method to reconstruct a time-varying is severely ill-conditioned. We solve the EIT with partial object modeled as a wide-sense stationary spatial ran- measurements using a numerical method based on the the- dom ﬁeld from its tomographic projections. The optimal ory of resistor networks and optimal grids, which does not reconstruction method combines aspects of the Kalman require explicit regularization. Two distinct variations of IS10 Abstracts 43

the method based on diﬀerent resistor network topologies how to use these conditions to reduce the arbitrariness, and and the theory of extremal quasiconformal mappings are to construct boundary functions with desired properties. presented. Ahmet Alturk Alexander V. Mamonov, Liliana Borcea Iowa State University Rice University [email protected] [email protected], [email protected] Fritz Keinert Vladimir Druskin Dept. of Mathematics Schlumberger Doll Research Iowa State University [email protected] [email protected]

CP2 CP3 Detection and Imaging Objects Buried Under a Discrete Symbol Calculus, a New Numerical Tool Rough Interface Through Experimental Data for Wave-Based Imaging The inverse scattering problem whose aim is to detect and Most linear operators that are somehow related to wave image the objects buried under a rough surface is solved propagation have an oscillatory integral representation and verified with the experimental data. By using the data that can be compressed by means of low-rank expansions which are collected through measurements performed on a of so-called symbols. We start by explaining this idea and line in the region not containing the bodies, it is first de- its implication for the numerical precomputation of func- tected and located the objects via the surface impedance tions of operators. We then show that this strategy yields a modelling. The surface impedance is calculated by ana- sensible way of numerically inverting the so-called normal lytically continuing the data to the rough interface. Then operator, or wave-equation Hessian, in reflection seismol- the contrast source extended Born approach is applied for ogy. Work in collaboration with Lexing Ying (UT Austin) the imaging of the objects, which requires to solve a cou- and Nicolas Boumal (MIT). pled system of integral equations. The Green function of the background media containing rough interface,which ap- Laurent Demanet pear in the integral equations, is calculated through Buried Mathematics, MIT Object Approach. [email protected]

Hulya Sahinturk Yildiz Technical University CP3 [email protected] Regularity Properties of Boundary Wavelets

Ibrahim Akduman Boundary functions for wavelets and multiwavelets on a ﬁ- Istanbul Technical University nite interval are usually constructed as linear combinations Electrical and Electronics Eng. Faculty of standard (interior) scaling functions. Such boundary [email protected] functions obviously inherit the smoothness properties of the interior functions. Boundary functions can also be constructed directly from recursion relations. We derive con- CP2 tinuity and approximation order conditions for this case. Shape-Based Methods for Vector-Valued Inverse This approach leads to new kinds of boundary functions, Problems with Highly Inhomogeneous, Unknown and lays the groundwork for the following talk on construc- Backgrounds tion of boundary wavelets. A variational formulation is developed for the recovery of Fritz Keinert multiple physical properties in an inverse problems con- Dept. of Mathematics text. A new, low-order parametric level set technique is Iowa State University employed to represent targets of interest embedded in an [email protected] inhomogeneous unknown background. Accurate recovery of this background is achieved through the use of a novel Ahmet Alturk regularization scheme coupling the multiple parameters of Iowa State University interest. The approach is validated for a dual energy X-ray [email protected] CT problem arising in an airport security application.

Oguz Semerci CP3 Tufts University Optimal Design for Imaging [email protected] Experimental design is an important topic for imaging science. It has broad applications in the areas of physics, biol- CP3 ogy and engineering. In this talk, we examine the Bayesian Construction of Boundary Wavelets AandAπ optimal designs. Our methods have the capability to improve the image quality while maintaining low We present a new approach for constructing boundary experimental cost. Several imaging experiments, such as functions for wavelets and multiwavelets on a ﬁnite inter- super resolution will be presented. Moreover, we explore val. The construction is unique up to the choice of some eﬃcient methods for large scale design problems. arbitrary orthogonal matrices. In the preceding talk Reg- ularity Properties of Boundary Wavelets we derived con- Zhuojun Magnant ditions for continuity and approximation order. We show Department of Mathematics and Computer Science 44 IS10 Abstracts

Emory University [email protected] [email protected] Peter B. Monk Eldad Haber Department of Mathematical Sciences Department of Mathematics University of Delaware The University of British Columbia [email protected] [email protected] Colton David Luis Tenorio University of Delaware Colorado School of Mines [email protected] [email protected] CP3 CP3 Reconstruction from Non-Uniform Spectral Data A Segmentation Boosted Denoising Scheme for Im- ages with Excessive and Inhomogeneous Noise We discuss the reconstruction of compactly supported piecewise-smooth functions from non-uniform samples of Image denoising is an important pre-processing step. It be- their Fourier transform. This problem is of relevance in comes a challenging task when the image contains excessive applications such as magnetic resonance imaging (MRI). and inhomogeous noise. It is especially hard to balance the We address the issue of non-uniform sampling density and preservation of features and removal of spatially variant its effect on reconstruction quality. We compare classical noise. To remove excessive noise, a single image denois- reconstruction approaches with alternate methods such as ing scheme usually leads to blurry images. We propose a spectral re-projection and methods incorporating jump in- method to take full advantage of information from segmen- formation. tation. The idea is explained using NL-Means framework. We use the original NL-Means to obtain an intermediate Adityavikram Viswanathan, Douglas Cochran result on which to apply segementation. The intensities School of Electrical, Computer and Energy Engineering and noise variances inside and outside the segmented ob- Arizona State University jects are then used to adaptive define search windows and [email protected], [email protected] smoothing parameters. They are utilied to the noisy image to obtain a clean and sharp image. The search windows Anne Gelb do not have a fixed geometry, they are however adaptively Arizona State University chosen inside or outside the objects to ensure identically [email protected] idenpendent distributed assumption to be better satisfied. Noise variances are calculated pointwisely to deal with in- Rosemary A. Renaut homogenity of noise. The proposed denoising scheme is Arizona State University fast and results in sharper images while removing exces- School of Mathematical and Statistical Sciences sive noise. [email protected] Weihong Guo Department of Mathematics, Case Western Reserve CP4 University Parametric Level Set Methods for Inverse Prob- [email protected] lems

Jing Qin PDE-based level set methods have difficulties in determin- Case Western Reserve University ing object structure for ill-posed inverse problems. A lack [email protected] of sensitivity can slow convergence. Grid-based representations lead to frequent re-initialization or the use of additional terms in the underlying cost function. We employ CP3 a parametric representation of the level set function using Analytical and Computational Methods for Trans- an adaptive expansion of compactly supported radial basis mission Eigenvalues function that addresses these difficulties. Results are presented using an electrical impedance tomography problem The interior transmission problem is a boundary value arising in environmental remediation. problem that arises in the scattering of time-harmonic waves by an inhomogeneous medium of compact support. Alireza Aghasi, Eric Miller The associated transmission eigenvalue problem has impor- Tufts University tant applications in qualitative methods in inverse scatter- [email protected], [email protected] ing theory. In this talk, we first establish optimal conditions for the existence of transmission eigenvalues for a spherically stratified medium and give numerical exam- CP4 ples of the existence of both real and complex transmis- Recovering the Location, Size, and Grade of a Car- sion eigenvalues in this case. We then propose three finite diac Ischemia Using Level Set Methods element methods for the computation of the transmission eigenvalues for the cases of a general non-stratified medium We present a level set strategy for recovering the character- and use these methods to determine the accuracy of re- istics of a cardiac ischemic region. Cardiac electrical activ- cently established inequalities for transmission eigenvalues. ity is modeled in 2-D with diffusion-reaction equations with different electrical behavior for the ischemic region and for the surrounding healthy tissue. Measurements are taken Jiguang Sun by electrodes outside of the cardiac membrane. Numerical Department of Mathematics, Delaware State University experiments show that the proposed strategy may stand for IS10 Abstracts 45

a practical algorithm to extract the diagnosis information ical mean value operator on the torus, which is the corner- of cardiac ischemia. stone of some recent imaging methods like photoacoustic tomography. We give a singular value decomposition of Diego Alvarez the this operator and characterize its range in terms of Universidad Carlos III de Madrid Sobolev spaces. Furthermore, we present a fast, Fourier [email protected] based algorithm for its numerical evaluation, give bounds for the discretization error, and compare our algorithm to Felipe Alonso-Atienza, JoséLuisRojo-Alvarez quadrature based algorithms. Universidad Rey Juan Carlos [email protected], [email protected] Ralf Hielscher Technische Universität Chemnitz, Germany Miguel Moscoso [email protected] Universidad Carlos III de Madrid [email protected] CP4 A Level Set Approach for Fluorescence Lifetime CP4 Tomography in Turbid Media Imaging Localized Scatterers with Singular Value The problem of fluorescence lifetime imaging involves the Decomposition and 1 Optimization reconstruction of the spatial distribution of the fluorescence We consider narrow band array imaging of localized scat- decay rates within the tissue simples from boundary data. In several centimiter thick tissue this problem poses several terers using the singular value decomposition (SVD) and 1 minimization and compare the results with other imaging challenges. In the direct problem one must account for methods such as multiple signal classification (MUSIC). multiple scattering of light in tissue, and in the inverse We show that well-separated point scatterers can be re- problem for the deconvolution of the pulse dispersion in the tissue and the fluorescence decay rates. In this talk covered exactly with 1 optimization. Moreover, using the SVD we determine optimally subsampled array data for we present an algorithm that is a hybridization of the level set technique for recovering the distributions of distinct the 1 optimization. Numerical simulations indicate that this imaging approach is robust with respect to additive fluorescent markers with a gradient method for estimating noise. If time permits, I will discuss comparison of differ- their lifetimes. ent imaging methods in random medium. Miguel Moscoso, Diego Alvarez, Paul Medina Anwei Chai Universidad Carlos III de Madrid Institute for Computational and Mathematical [email protected], [email protected], pmed- Engineering [email protected] Stanford University [email protected] CP5 Image Processing Techniques for Assessing Con- George C. Papanicolaou tractility in Isolated Adult and Neonatal Cardiac Stanford University Myocytes Department of Mathematics [email protected] We describe two computational frameworks to assess the contractile responses of enzymatically dissociated adult and neonatal cardiac myocytes. Our results demonstrate CP4 the effectiveness of the approaches in characterizing the Regularization Parameter Selection for Penalized- true ”shortening” in the contraction process. The meth- Maximum Likelihood Estimation Methods in Pet. ods provide comprehensive assessment of the contraction process, and can potentially eliminate errors caused by ro- PET data consists of counts of photons originating from tation or translation. Changes due to drug intervention, random events, resulting in data-noise that is well-modeled disease modeling, transgeneity, or other common applica- by a Poisson distribution. Since the associated Poisson tions to mammalian cardiocytes can be evaluated. maximum likelihood estimation problem is ill-posed, regularization is needed. Regularized Poisson maximum like- Peter Blomgren lihood estimation has been extensively studied by the au- San Diego State University thors, however, the essential problem of choosing the regu- Department of Mathematics and Statistics larization parameter remains unaddressed. In this talk, we [email protected] present three statistically motivated methods for choosing the regularization parameter. Numerical examples will be Carlos Bazan presented to test these methods. San Diego State University John Goldes Computational Science Research Center Department of Mathematical Sciences [email protected] University of Montana [email protected] David Torres Computational Science Research Center San Diego State University CP4 [email protected] Numerical Inversion of the Spherical Mean Value Operator Paul Paolini Department of Biology We are concerned with the numerical inversion of the spher- San Diego State University 46 IS10 Abstracts

[email protected] through analytical means.

Cheng Guan Koay, Evren Ozarslan CP5 Section on Tissue Biophysics and Biomimetics, NICHD Atlas Based Mri Segmentation Using Both Magni- National Institutes of Health tude and Phase Information [email protected], [email protected]

We present a new framework for MR image segmentation Peter J. Basser based on deformable template using both the magnitude National Institutes of Health and phase information. In VASO MRI, the phase depends [email protected] on tissue type, provides extra information about object boundaries. Hence using phase information will improve Carlo Pierpaoli the segmentation and analysis of MR images. Finding the Section on Tissue Biophysics and Biomimetics, NICHD optimal mapping is formulated as a variational problem National Institutes of Health over a vector ﬁeld. [email protected] Yan Cao The University of Texas at Dallas CP5 Department of Mathematical Sciences [email protected] Detecting Jump Discontinuities Given Noisy Fourier Data

Jinsoo Uh, Hanzhang Lu The detection of jump discontinuities in physical space us- UT Southwestern Medical Center ing frequency (Fourier) data is an essential aspect of Medi- [email protected], cal Resonance Image processing. The difficulty of the task [email protected] lies in extracting local information from the global Fourier data, and is further complicated by noise. In this talk, we discuss a recently developed algorithm that uses frequency CP5 data to recover the jump discontinuities. The expected ac- Physics-Based Image Segmentation for Endoscopic curacy of the detector has been modeled using statistical Images hypothesis testing. We propose a new mathematical model for analyzing endo- Alexander M. Petersen scopic images, which are obtained in vivo by chromoscopic Arizona State University colonoscopy. The model is based on a PDE-constrained [email protected] optimization problem, in which the state equation represents the chromoscopy process and the objective function uses the Chan and Vese segmentation model. CP5 A Study of Chiari Malformations Using Magnetic Isabel N. Figueiredo Resonance Elastography University of Coimbra [email protected] Magnetic Resonance Elastography (MRE), also called pal- pation by imaging, is a non-invasive, in vivo imaging tech- Omar Ghattas, Georg Stadler nique used to measure the elasticity of a biological tissue University of Texas at Austin subject to dynamic or static mechanical stress. The result- [email protected], [email protected] ing strains are measured using magnetic resonance imaging (MRI) and the related elastic modulus is computed from Pedro Figueiredo models of tissue mechanics. Such a technique can be used Faculty of Medicine, University of Coimbra not only as a non-invasive diagnostic tool for tumor detec- Portugal tion, but also for gaining fundamental knowledge about the pedro.n.fi[email protected] in vivo mechanical properties of normal biological tissues. In particular, brain MRE using the natural pulsations of Nuno Almeida the brain will help us better understand the brain mechan- Department of Gastroenterology ics. The present proposal will involve using magnetic res- University Hospital of Coimbra, Portugal onance images from Hershey College of Medicine of brains [email protected] of patients with chiari malformations. We plan to analyze how the presence of this malformation changes the stiffness of the brain tissue in the vicinity of the malformation. The CP5 design aim of the proposal is to develop a computational Probabilistic Identification and Estimation of Noise tool in Matlab capable to study the mechanical proper- (piesno): Mathematical Features and Challenges ties of the brain tissue with chiari malformations before and after the surgery using medical images and appropri- PIESNO is a recent technique of noise assessment for mag- ate mechanical models for the brain. netic resonance imaging that has provided new approach to identifying noise-only pixels and to estimating noise level Osman Veledar in magnitude images. This technique embodies common The Penn State University features from different fields such as probability and dy- [email protected] namical system. Here, we will outline these interesting features and discuss key mathematical challenges associ- Corina Drapaca ated with this framework that are currently not tractable Department of Engineering Science and Mechanics Pennsylvania State University [email protected] IS10 Abstracts 47

CP5 CP6 Fast Algorithm for Sensitivity Encoding with Ar- Counterexamples in Image Deconvolution bitrary K-Space Trajectories Image deconvolution requires regularization. This talk will Speed is a crucial issue in MR imaging for clinical appli- survey a number of reasonable regularization approaches cations. We propose a fast numerical algorithm for Sensi- that nevertheless lead to unsatisfactory results. tivity Encoding in partial parallel imaging with arbitrary k-space trajectories. The proposed method is an integra- Alfred S. Carasso tion of the variable-splitting and penalty techniques (VSP) Nat’l Inst of Standards & Tech with Barzilai-Borwein (BB) gradient method. VSP formu- [email protected] lates the original model as an unconstrained minimization problem, which can be split into two subproblems: TV denoising and linear inversion. The former can be solved CP6 efficiently using recently developed methods, whereas the Parallel Denoising optimal solution for the latter can be quickly approximated by using BB method. Continuation scheme is also used to New frontiers of science are creating huge demands on com- improve the practical performance. Comparisons with var- putational imaging. Biological studies aiming to reveal the ious recently proposed methods indicate the outstanding inner works of cells and cell-to-cell interactions rely on ul- efficiency of our algorithm with state-of-the-art reconstruc- tra resolution images to observe when, where, and how a tion effects. Our method can be extended to any TV/L1 cell develops so we can understand with the help of fac- image reconstruction problems. tual observations the entire mechanisms of cell regulation. Astronomy will enourmesly benefit from the planned 3.2 Xiaojing Ye Gigapixel camera of the Large Synoptic Survey Telescope. Department of Mathematics, University of Florida The project will generate images of the sky covering bil- 358 Little Hall, Gainesville, FL32611-8105 lions of galaxies and stars at a rate of 15 Terabytes per xye@ufl.edu night. In both situations fast and reliable image processing is required to render solutions in a reasonable time. To Dzung Phan cope with such challenging processing demands we devel- Department of Mathematics oped NOIR, Nonlinear Image Restoration software. NOIR University of Florida is a parallel image denoising algorithm and software capa- dphan@ufl.edu ble of filtering images at an approximate rate of 3.5 million pixels per second on a commodity 16 cores computer. It is based on our rewriting of the nonlocal means filter. We Yunmei Chen will present our algorithm and show how we make such a University of Florida remarkable filter useful for projects in Biology, Astronomy, [email protected]fl.edu and Materials Science. Feng Huang Alexandre Cunha Invivo Corporation, Philips HealthCare, Gainesville, FL California Institute of Technology [email protected] [email protected]

Jerome Darbon CP6 UCLA A New Model for Deblurring Images [email protected] We propose a new model for recovering an image from a blurry observation. This model is based on a new form of CP6 the blur operator and consists to solve a particular opti- A Robust Method for Joint Correction of Nonuni- mization problem which is intimately linked to the moment form Illumination and Blind Deconvolution of Bar- problem. We combine recent mathematical results on mo- code Signals ments and semidefinite programming to provide a reliable skill for deblurring images. The methodology allows to This paper deals with a joint nonuniform illumination esti- handle isotropic and anisotropic blur. mation and blind deconvolution for barcode signals. Such optimization problems are highly non convex. A robust Tahar Zamène Boulmezaoud method is needed in case of noisy and blurred signals and Laboratoire de Mathématiques de Versailles uneven illumination. Here, we present a novel method University of Versailles SQY based on a genetic algorithm combining discrete and con- [email protected] tinuous optimization. It is successfully applied to real datas with strong noise. A comparison with a non local gradient Mohamed El Rhabi based method is also provided. Realeyes 3D Corp. Saint-Cloud, France Laurent Dumas [email protected] Universite Pierre et Marie Curie Paris 6 [email protected] Gilles Rochefort RealEyes3D Mohammed El Rhabi, Gilles Rochefort [email protected] RealEyes3D [email protected], [email protected] 48 IS10 Abstracts

CP6 Institute for Computational and Mathematical Image Denoising and Restoration by Constrained Engineering Regularization Stanford University [email protected] In this work we present a new iterative algorithm for image deblurring and denoising. The algorithm is based on the solution of the constrained least squares problem: CP7 Compressed Sensing Synthetic Aperture Radar δ min Hx − y 2 s.t. R(§) ≤ γ, γ > Imaging We introduce a new Synthetic Aperture Radar (SAR) where the smoothness constraint γ is computed by an ef- δ imaging modality which can provide a high resolution map ficient low pass filtered version of the noisy data y .The of the spatial distribution of targets and terrain based on iterations compute an approximate value of the Lagrange using a significantly reduced number of needed transmit- multiplier λ and the solution x(λ). The method has been R § ted and/or received electromagnetic waveforms. This new widely tested with different regularization functions ( ) scheme allows the aperture to be compressed and presents in case of gray levels and color images. many new advantages which include strong resistance to Fabiana Zama countermeasures and interception, imaging much wider Department of Mathematics, University of Bologna swaths, and reduced on board storage constraints. [email protected] Glenn Easley Systems Planning Corporation Elena Loli Piccolomini [email protected] Department of Mathematics, University of Bologna Vishal Patel, Dennis Healy, Rama Chellappa [email protected] University of Maryland [email protected], [email protected], [email protected] CP6 Blind Restoration from Mild Blur and Heavy Noise CP7 We present a non-iterative algorithm for blind restoration Multiple Measurement Vector Problem with of an image which has been corrupted by mild blur, and Subspace-Based Algorithm strong noise. The most successful deblurring algorithms to In multiple measurement vector problem, we consider the date address the problem in a setting where the corrupting problem of the recovery of vectors which have common noise is assumed so small as to be essentially negligible. Un- sparsity patterns. First, when we have sufficient number fortunately, in practical applications, much stronger noise of measurements, we can recover the jointly sparse vectors is often present, which renders most algorithms useless. with a MUSIC-style algorithm. Then we propose a varia- Furthermore, it is often the case that most images we wish tion of MUSIC-style subspace-based algorithm to recover to enhance in practice suffer from mild, rather than severe the jointly sparse vectors efficiently when we have insuffi- blur. This motivates our study, where we develop a lo- cient number of random measurements or noisy measure- cally adaptive and non-parametric method for high fidelity ments. enhancement of such distorted images. We illustrate that our algorithm can produce state of the art results under Jong Min Kim,JongChulYe practical imaging conditions. KAIST [email protected], [email protected] Xiang Zhu University of California, Santa Cruz [email protected] CP7 Sparse and Fast Fourier Transforms in Biomedical Peyman Milanfar Imaging EE Department University of California, Santa Cruz A straightforward discretization of high dimensional prob- [email protected] lems often leads to a serious growth in the number of degrees of freedom and thus even efficient algorithms like the fast Fourier transform have high computational costs. Uti- CP7 lizing sparsity allows for a severe decrease of the problem Tracking and Autofocus in Synthetic Aperture size but asks for the customization of efficient algorithms Radar Imaging to these thinner discretization. We discuss modern gen- eralizations of the FFT and their application in emerging From first principles, we develop a synthetic aperture radar imaging modalities like photoacoustic tomography. imaging method that includes both motion estimation of targets and radar platform trajectory estimation. The Stefan Kunis method uses both the Wigner transform and ambiguity Chemnitz University of Technology function of the radar data and preliminary images, prop- Faculty of Mathematics erly segmented over sub-apertures, to derive estimates for [email protected] the target motion and platform perturbations. This approach produces an iterative method to construct autofo- cused high-resolution images over wide apertures, applica- CP7 ble to X-band persistent surveillance SAR. Compressive Radar Imaging Thomas Callaghan In this article, far-field space-time radar imaging problems IS10 Abstracts 49

are formulated in the framework of compressive sensing. construct a functional with variable exponent which allows The recoverability of detecting point scatterers, located on each pixel to belong to each image pattern with different a lattice searching plane, is analyzed by the mutual coher- probability and combines the TV-based and isotropic diffu- ence of the sensing matrix which is constructed from de- sion. By taking different Gaussian means and variances on signing signal waveform and radar imaging formulation. It each image pattern, the segmentation becomes more accu- is shown that the coherence of the sensing matrix is highly rate. Numerical examples of natural and synthetic images related to the choice of the waveform, and the sensing po- are presented to illustrate the use of the model. sition due to the grid structure. Numerical experiments of recoverability by pursuits are also provided. Iulia Posirca, Yunmei Chen University of Florida Hsiao-Chieh Tseng [email protected]fl.edu, [email protected]fl.edu Dept. of Math, UCDavis [email protected] Celia A. Barcelos Universidade Federal de Uberlandia Uberlandia, MG - Brazil CP8 [email protected] A New Variational Edge Representation for Image Segmentation Using Active Contours CP8 We consider an approach to segmentation motivated by Supervised Segmentation of Multi-Banded Image the Chan-Vese idea of minimizing a linear combination Data Using Statistically-Based Methods of the pixel variances inside and outside a contour. Our method maximizes the contrast between inside and out- Both spatial and non-spatial statistically-based classifica- side pixel averages relative to an adaptively defined inter- tion methods are explored on the problem of segmenting mediate value. The model is easier to configure the free imagery. For the learning step, in which training data is parameters than that of Chan-Vese while demonstrating used to build the classifier, we use quadratic discriminant the efficiency and comparing the performances on a range analysis. Training data is obtained from the image we wish of image data. to classify using a MATLAB graphical user interface (GUI) created by us for this purpose. Post classification smooth- Alireza Aghasi, Bruce M. Boghosian, Eric Miller ing is implemented using nonlinear filtering, probability Tufts University label relaxation, and Markov random fields. [email protected], [email protected], [email protected] Marylesa Wilde, John Bardsley The University of Montana [email protected], [email protected] CP8 Spectral Segmentation of Polygonized Images with Chris Gotschalk Normalized Cuts UC Santa Barbara We present an implementation of the Normalized Cuts [email protected] method adapted for spectral segmentation of polygonized images. We make novel observations regarding the effects Mark Lorang of the rounding errors on the Fiedler solution and other The University of Montana eigenvectros of the affinity matrix when computations are [email protected] carried out in finite precision. These observations motivate us to partition the image in the multidimensional space spanned by the transposed matrix of the few of the lowest CP8 eigenvectors of the affinity matrix. We develop a new low Nonparametric Image Segmentation Using Rényi’s complexity implementation of the Mean Shift method in Statistical Dependence Measure order to produce meaningful and efficient clustering of the computed eigenvector subspace. We conduct a compara- We present a novel nonparametric image segmentation ap- tive study of the developed method with the Multiscale proach, which partitions an image by maximizing the sim- Normalized Cuts and Segmentation by Weighted Aggre- ilarity between that image and its label image. Rényi’s gation methods that demonstrates comparable and even statistical dependence measure, maximum cross correla- superior performance of the proposed method. tion (MCC), is employed to measure the similarity. MCC deals only with samples and does not need to estimate the Anna Matsekh, Alexei Skurikhin continuous joint probability density function, which is sen- Los Alamos National Laboratory sitive to image quantization and makes the optimization [email protected], [email protected] process complex. The computation is further simplified by the theory of reproducing kernel Hilbert spaces. Edward Rosten Haili Zhang, Yunmei Chen University of Cambridge Department of Mathematics [email protected] University of Florida hlzhang@ufl.edu, yun@ufl.edu CP8 A Soft Segmentation Model Using Functionals with Jiangli Shi Variable Exponent University of Florida [email protected] We propose here an efficient soft Mumford-Shah stochastic model for segmentation of a mixture patterns image. We 50 IS10 Abstracts

MS1 either frame-by-frame or inter-frame difference recovery Distributed Compressive Imaging methods. We consider the problem of compressive imaging for dis- Michael B. Wakin tributed imaging sensors. Distributed Compressive Imag- Division of Engineering ing offers joint image compression/reconstruction from Colorado School of Mines imaging sensors which have overlapping fields-of-view. [email protected] When viewed as a composite image sampling mechanism, a network of imaging sensors could transmit dramatically less data than current technologies while maintaining or MS2 surpassing image reconstruction quality of the underlying Full Wave Equation Depth Extrapolation for Mi- scene. We present performance results as a function of the gration number of cameras, transmission bandwidth, and camera perspective registration accuracy. Using the full wave equation for depth wave-field extrapolation leads to an ill-posed problem. In avoiding the blow-up Chris Huff of evanescent waves, a typical downward extrapolation in Department of Mathematics a variable background uses approximate one-way propaga- University of Central Florida tors and partially suppresses useful propagating waves, e.g., chrishuff[email protected] generated by steep reflectors. Recently, we developed a new algorithm for downward extrapolation which removes only the evanescent waves and leaves all propagating modes in- MS1 tact. Numerical experiments confirm significant improve- CS Imaging Applications and Challenges ments in seismic migration using our approach.

We developed an optical imaging technique based on com- Gregory Beylkin pressive sensing. One area where we have implemented Univ. of Colorado, Boulder this system is infrared imaging where the advantages in- [email protected] clude lower costs and higher sensitivity. The same system architecture is also employed in hyperspectral compressive Kristian Sandberg sensing imaging with the potential to go directly from mea- GeoEnergy, Corp. surements to identification without the need to reconstruct [email protected] the entire hyper cube. Lastly, a compressive sensing echelle spectrometer has been also been built. MS2 Kevin Kelly Imaging with Multiply Scattered Waves: Remov- Electrical and Computer Engineering Department ing Artifacts Rice University [email protected] The majority of seismic imaging assumes the single- scattering approximation, which linearizes the inverse problem. When recorded data do not satisfy this assump- MS1 tion artifacts appear in the computed images. In specific Compressive Imaging for Target Tracking methods for imaging using multiply-scattered waves, singly scattered waves produce similar artifacts in the resulting We consider the application of compressive imaging theory images. We will discuss new techniques for estimating and to the problem of persistent surveillance. As compressive removing these artifacts in the context of one-way methods sensing enjoys significant research attention, application for seismic imaging. areas for compressive imaging are becoming clearer. We highlight several prospective compressive imaging applica- Alison Malcolm tions which could increase current performance by orders MIT of magnitude. Each application has algorithm and hard- [email protected] ware implications which will be discussed. Specifically, we present expanded field-of-view imaging, expanded frame Maarten de Hoop rate video, exploitation while sensing, and multiplatform Center for Computational & Applied Mathematics image fusion. Purdue University [email protected] Robert R. Muise Lockheed Martin [email protected] Bjorn Ursin Norwegian University of Science and Technology [email protected] MS1 A Multiscale Framework for Compressive Sensing MS2 of Video Operator Upscaling for Seismic Inversion We consider the application of Compressive Sensing (CS) to video signals. In standard video compression, motion While upscaling has been studied extensively for reservoir compensation techniques have led to improved sparse rep- simulation, its use for wave propagation is less common, resentations; we adapt these techniques for CS recovery. despite the inherent multiscale character of the subsurface. Using a coarse-to-fine reconstruction algorithm, we alter- Inversion studies typically rely on settling on a single scale nate between motion estimation and motion-compensated of interest in estimated material parameters. We investi- wavelet-domain signal recovery. Our algorithm allows the gate using a two-scale solution algorithm for the acoustic recovery of video sequences from fewer measurements than wave equation as a forward simulator for inversion. The IS10 Abstracts 51

two-scale algorithm parallelizes with almost no communi- Xiaoqun Zhang cation and captures sub-wavelength heterogeneities on the University of California Los Angeles. coarse scale. [email protected]

Susan E. Minkoﬀ Tony Chan University of Maryland, Baltimore County University of California. Los Angeles Dept of Mathematics and Statistics [email protected] sminkoﬀ@umbc.edu

MS3 MS2 Subspace Correction Methods for 1 and Total Image Amplitudes in Wave Equation Imag- Variation Minimization ing/inversion In the context of compressed sensing and sparse recovery, Wave equation imaging often yields structurally correct im- it has been clarified that the minimization of 1-norms oc- ages of the Earth. However, it is more difficult to obtain cupies a fundamental role for the promotion of sparse so- the correct amplitude for the structures in the image. Here lutions. This understanding furnishes an important inter- I present recent progress in this problem. Topics will be (1) pretation for total variation minimization, i.e., the mini- the estimation of position and direction dependent scaling mization of the L1-norm of derivatives, as a regularization factors by which to correct image amplitudes, and (2) the technique for image restoration. These minimizations are case of a single source, where we can derive a microlocal typically nonsmooth and are performed with algorithms inverse. whose convergence is usually proved by compactness ar- Christiaan C. Stolk guments; in particular there are no guaranteed rates of University of Amsterdam convergence in general. For very large scale problems se- [email protected] quential algorithms fail to approximate minimal solutions in acceptable computational time. Therefore it is desirable to consider domain decomposition or subspace correction MS3 strategies. In presence of nonsmooth convex constraints Improved Dynamic PET via Kinetic Models and which are not splitting additively with respect to a decom- Operator Splitting position, it is well known that such strategies will fail to converge to minimizers in general. In this talk we present Dynamic Positron Emission Tomography allows monitor- several new results of convergence for domain decomposi- ing physiological processes within the body that can be tion and subspace correction methods specifically tailored described by kinetic parameters. However, recovery of for 1-norm and total variation minimization. We will also these parameters often requires the solution of complex and present counterexamples for situations where this strategy nonlinear operator equations. Advanced operator split- fails. We illustrate the theoretical results by presenting ting techniques allow incorporating a-priori knowledge, e.g. several numerical examples. sparsity of minimizers with respect to an exponential basis, into the reconstruction process. Massimo Fornasier Johann Radon Institute for Computational and Applied Martin Benning Mathematics (RICAM) Institute for Computational and Applied Mathematics [email protected] University of Muenster [email protected] MS3 Recent Numerical Methods for Large-scale Prob- MS3 lems in Imaging Applications An Explicit Primal-Dual Algorithm for Large Non- Differentiable Convex Problems In this presentation I shall give an overview about recent advances in the efficient numerical solution of total varia- In this talk, based on joint work with Xiaoqun Zhang and tion minimization for large-scale imaging applications. Tony Chan, I will discuss a modification of the primal- dual hybrid gradient (PDHG) algorithm proposed by Zhu Carola-Bibiane Schönlieb and Chan. The PDHG method applied to a saddle point Institute for Numerical and Applied Mathematics formulation of a convex minimization problem proceeds by Georg-August University of Goettingen alternating proximal steps that maximize and minimize pe- [email protected] nalized forms of the saddle function. This can be useful for producing explicit algorithms for large non-differentiable MS4 convex problems, and a slight modification to the method can be made to guarantee convergence. For the problem Diffeomorphic Image Registration using Gauss- of minimizing sums of convex functionals composed with Newton Optimisation linear operators, I will show how to use operator splitting This work frames image registration in terms of estimat- techniques that allow the modified PDHG method to be ef- ing MAP or regularised maximum likelihood solutions for fectively applied. Specific applications to constrained TV the deformations. Diffeomorphic deformations are param- deblurring and compressive sensing problems will be pre- eterised by their initial velocities, which are estimated via sented. a Gauss-Newton optimisation scheme. At each iteration, Ernie Esser the coefficients parameterising the initial velocity are in- UCLA Mathematics Department cremented by a matrix division of the first derivatives by University of California Los Angeles the (expectation of the) second derivatives. The solution [email protected] for this division is obtained using a multigrid approach. 52 IS10 Abstracts

Images are assumed to consist of binary labelled regions, the images are observed with noise. and the template encodes the mean of the multinomial distributions from which the images are drawn. The template Jean-Michel Loubes is modelled by a Gaussian process (over 3D space) that is Equipe de Statistique et Probabilités UMR 5219 ”squashed” using a softmax function. Université de Toulouse 3, Institut de Mathématiques [email protected] John Ashburner Wellcome Trust Centre for Neuroimaging Functional Imaging Laboratory MS4 john@fil.ion.ucl.ac.uk Statistical Analysis of Anisotropic Brownian Image Textures MS4 In this talk, I focus on the analysis of anisotropy in image Statistical Analysis of Neuroanatomy textures. To deal mathematically with this issue, I present a statistical framework gathering some anisotropic exten- A primary goal of Computational Anatomy is the statisti- sions of the fractional Brownian field. In this framework, cal analysis of anatomical variability. A natural question I give several asymptotic results about the estimation of that arises is how does one define the image of an ”Average model parameters and the testing of anisotropy. I also Anatomy”. Such an ”average” must represent the intrin- present some applications to bone X-ray images and mam- sic geometric anatomical variability present. Large De- mograms. formation Diffeomorphic transformations have been shown to accommodate the geometric variability but performing Frederic Richard statistics of Diffeomorphic transformations remains a chal- MAP5 - UMR CNRS 8145 lenge. In this lecture I will further extend this notion of University Paris Descartes averaging for studying change of anatomy on average from [email protected] a cross sectional study of growth. Regression analysis is a powerful tool for the study of changes in a dependent variable as a function of an independent regressor variable, MS5 and in particular it is applicable to the study of anatom- A Variational Approach to Blind Image Deconvo- ical growth and shape change. When the underlying pro- lution cess can be modeled by parameters in a Euclidean space, classical regression techniques are applicable and have been Blind Image Deconvolution is a challenging problem on studied extensively. However, recent work suggests that at- which much recent progress has been made. In my talk tempts to describe anatomical shapes using flat Euclidean I will describe a regularization scheme based on image- spaces undermines our ability to represent natural biolog- gradient priors and explain its use in a variational frame- ical variability. In this lecture I will develop a method for work. I will to explain why conventional MAP formula- regression analysis of general, manifold-valued data. Fur- tions yield degenerate solutions and how a variational ap- ther more I will extend the notion of Robust estimation to proaches can avoid them, enabling good quality results to Manifold valued data. The Median is a classic robust esti- be recovered. mator of centrality for data. In this lecture I will formulate Rob Fergus the geometric median of data on a Riemannian manifold as New York University the minimizer of the sum of geodesic distances to the data [email protected] points. I will exemplify the robustness of the estimation technique by applying the procedure to various manifolds commonly used in the analysis of medical images. Using MS5 this approach, we also present a robust brain atlas estima- Variational Formulation for Nonlocal Image De- tion technique based on the geometric median in the space blurring with Collaborative l0-Norm Prior of deformable images. Non-local patch-based estimation is currently one of the Sarang Joshi most promising directions in image processing. Within this Scientific Computing and Imaging Institute framework, a number algorithms has been developed for University of Utah different imaging problems and particularly for image de- [email protected] noising, where the BM3D filters represent the state-of-the- art in terms of quality (Katkovnik et al., Int. J. Computer MS4 Vision, 86(1) 1-32, 2010). We recently proposed a special prior which allows to reformulate the multistage BM3D Statistical Analysis of Image Warping Issues with hard-thresholding as minimization of a global energy cri- M-estimation terion (Katkovnik, TICSP Series 47, 305-319, 2009). This A current trend is the study of probabilistic and statisti- prior was further developed as a tool for the design of very cal aspects of deformation models, and the development of efficient deblurring algorithms in which the collaborative consistent statistical procedure for the estimation of tem- l0-norm penalty works as a spatially adaptive regulariza- plate images. We consider a set of images randomly warped tor (Katkovnik and Egiazarian, Proc. LNLA2009). The from a mean template which has to be recovered. For this, main contribution presented in this talk concerns the de- we fisrt consider a semiparametric framework and show velopment and testing of a frequency-domain recursive al- that minimization a well-suited contrast can lead to effi- gorithm minimizing the collaborative nonlocal l0-norm cri- cient estimatots; then in a non parametric framework, un- terion. Simulations demonstrate a very good performance der an appropriate statistical parametric model to generate of the algorithm. random diffeomorphic deformations in two-dimensions, we Vladimir Katkovnik, Karen Egiazarian focus on the problem of estimating the mean pattern when Tampere University of Technology vladimir.katkovnik@tut.fi, karen.egiazarian@tut.fi IS10 Abstracts 53

Alessandro Foi Washington University Department of Signal Processing [email protected] Tampere University of Technology, Finland alessandro.foi@tut.fi Aseem Agarwala Adobe Systems [email protected] MS5 Optimizing the Blur-Noise Tradeoff with Multiple- Photo Capture MS5 Superresolution and Blind Deconvolution of Video Capturing multiple photos at different focus settings is a powerful approach for reducing optical blur, but how In many real applications, traditional superresolution many photos should we capture within a fixed time bud- methods fail to provide high-resolution images due to ob- get? We develop a framework to analyze optimal cap- jectionable blur and inaccurate registration of input low- ture strategies balancing the tradeoff between defocus and resolution images. In this talk, we present a method of su- sensor noise, incorporating uncertainty in resolving scene perresolution and blind deconvolution of video sequences depth. We derive analytic formulas for restoration error and address problems of misregistration, local motion and and use Monte Carlo integration over depth to derive opti- change of illumination. The method processes the video by mal capture strategies for different camera designs, under applying temporal windows, masking out regions of mis- a wide range of photographic scenarios. We also derive a registration, and minimizing a regularized energy function new upper bound on how well spatial frequencies can be with respect to the high-resolution frame and blurs, where preserved over the depth of field. Our results show that regularization is carried out in both the image and blur by capturing the optimal number of photos, a standard domains. Experiments on real video sequences illustrate camera can achieve performance at the level of more com- robustness of the method. plex computational cameras, in all but the most demand- ing of cases. We also show that computational cameras, Filip Sroubek, Jan Flusser although specifically designed to improve one-shot perfor- Czech Academy of Sciences mance, generally benefit from capturing multiple photos as [email protected], fl[email protected] well. http://www.cs.toronto.edu/ hasinoff/timecon/

Sam Hasinoﬀ MS6 MIT Impact of JPEG Compression and Resolution De- Computer Science and AI Lab creasing in Stereo Accuracy hasinoﬀ@csail.mit.edu In this work, we quantitatively study the impact of JPEG Kiriakos Kutulakos compression in stereo accuracy. We compare this accu- University of Toronto racy with the one obtained by a convolution+subsampling Computer Science compression strategy. We show that for the same rate of [email protected] compression a better accuracy is obtained by this latter strategy. Fredo Durand Bartomeu Coll Massachusetts Institute of Technology Universitat Illes Balears [email protected] [email protected]

William Freeman Antoni Buades MIT Paris Descartes Computer Science and AI Lab [email protected] [email protected] Jean-Michel Morel, Bernard Rouge MS5 ENS Cachan Deblurring with Advanced Optimization [email protected], [email protected]

We present a deblurring method using advanced optimization to alternate between blur kernel estimation and un- MS6 blurred image restoration. We present an analysis of the Variational Methods Stereo and Multi-view Recon- causes of common artifacts found in current deblurring struction methods, and then introduce several terms that are useful in deblurring. These terms include a model of the I will address the shape optimization challenges in stereo spatial randomness of noise in the blurred image, as well and multiview reconstruction by means of variational a local smoothness prior that reduces ringing artifacts by methods. I will show that multiple view reconstruction constraining contrast in the unblurred image wherever the and stereo depth estimation can be solved by minimizing blurred image exhibits low contrast. Finally, we describe convex functionals over convex domains. This allows to an eﬃcient optimization scheme. compute globally optimal solutions which are independent of initialization and of the choice of minimization strat- Leo Jiaya Jia egy. Furthermore, I will present the ﬁrst super-resolution The Chinese University of Hong Kong algorithm for texture estimation in the multiview context. [email protected] Daniel Cremers, Kalin Kolev, Bastian Goldluecke Qi Shan Department of Computer Science 54 IS10 Abstracts

University of Bonn a classical minimization problem. The energy to be min- [email protected], [email protected], imized involves the inner product cost of observed local [email protected] deformations (reliable matchings between close shapes) as well as a regularization term based on transport of defor- Thomas Pock mations and Kullback-Leibler divergence. Surprisingly, the Institute for Computer Graphics and Vision global minimum of this functional on metrics is related to Graz University of Technology principal component analyses and is easy to compute. [email protected] Guillaume Charpiat PULSAR team - INRIA MS6 [email protected] A Contrario Image Matching: Shape-elements, Shape-Context, SIFT, PCA MS7 In image matching problems we are confronted to decide Spatiotemporal Atlas Building via Frechet Means whether two descriptors are alike or not. In situations of Diffeomorphisms where a model of the structure to be detected cannot be estimated, the a-contrario methodology based on controling The construction of average models of anatomy, as well as the number of false alarms (NFA) leads automatic detec- regression analysis of anatomical structures, are key issues tion thresholds. In this talk we present a general technique in medical research, e.g., in the study of brain develop- to obtain accurate estimates of the NFA, and its applica- ment and disease progression. However, anatomical shape tion to secure matches of image level lines, patches, SIFT change is often modeled using transformations—such as or Shape-Context. the group of diffeomorphisms—that do not form a linear space. This talk describes methods for defining averages Pablo Musé and kernel-based regression for anatomical structures via Facultad de Ingeniera - Universidad de la Repblica the Fréchet mean and a diffeomorphism-based metric. Uruguay pmuse@fing.edu.uy Brad Davis Kitware. Inc. [email protected] MS6 Optimal Stereo Matching Reaches Theoretical Ac- MS7 curacy Bounds Conformal and Multi-scale Metrics on Shape This talk will focus on accuracy in block-matching for Spaces stereo-rectified images and how the disparity map can be computed for a majority of image points up to a 1/20 pixel We will present several families of metrics on curves and precision. A theoretical prediction of the errors caused by surfaces, each of which is based on some multi-scale repre- noise will be given, and it will be proved on several simu- sentation and is equivalent to a Sobolev-type norm. These lated and real experiments that this bound is reached by metrics measure local regularity of a curve or surface, with the proposed algorithm. Experiments on the Middlebury explicit recognition of the role played by scale. We will benchmark show that the presented method improves the present both theoretical and experimental results. precision of the ground truth. Matt Feiszli Neus Sabater Yale, Mathematics CMLA - ENS Cachan [email protected] France [email protected] MS7 A Computable Formulation of Curvature for the Andrés Almansa Riemannian Manifold of Landmarks Telecom ParisTech & CNRS [email protected] In the past few years there has been a growing interest, in diverse scientific communities, in endowing ”shape spaces” Jean-Michel Morel with Riemannian metrics, so to be able to measure simi- ENS Cachan larities between shapes and perform statistical analysis on [email protected] data sets (e.g. for object recognition, target detection and tracking, classification, and automated medical diagnos- tics). The geometry of such spaces has started to emerge MS7 only very recently; in this talk we will explore the sec- Estimating Suitable Metrics for an Empirical Man- tional curvature for the Riemannian manifold of landmark ifold of Shapes points (which is one of the simplest, in that it is finite- dimensional) and discuss its effects on applications. We propose a framework to learn shape metrics from a set of examples of shapes, able to handle sparse sets of highly Mario Micheli varying shapes, like human silhouettes. The tangent space UCLA– Mathematics of a shape being the set of all infinitesimal deformations [email protected] that can be applied to it, an inner product in a tangent space can be seen as a deformation prior, and thus as a Gaussian distribution. We formulate the task of finding the MS8 optimal metrics, i.e. the inner products in tangent spaces Fast Sensitivity Encoding with Arbitrary k-space which suit the best a given empirical manifold of shapes, as IS10 Abstracts 55

Trajectories in Partial Parallel Imaging MS8 Efficient Global Optimization for the Multiphase Speed is a crucial issue in MR imaging in many clinical Chan-Vese Model of Image Segmentation by Graph applications. This paper presents a fast reconstruction Cuts algorithm of Sensitivity Encoding with arbitrary k-space trajectories to improve the clinical applicability of partial The Mumford-Shah model is an important variational im- parallel imaging (PPI). The proposed method combines the age segmentation model. A popular multiphase level set variable-splitting and quadratic penalty techniques in op- approach, the Chan-Vese model, was developed for this timizations with an accelerated gradient method. By us- model by representing the phases by several overlapping ing variable-splitting and penalty techniques the original level set functions. Recently, binary level set functions model can be reformulated as an unconstrained minimiza- were proposed as a variant representation of the Chan-Vese tion problem, whose minimizers can be computed by solv- model. In both approaches, the gradient descent equations ing a TV denoising problem and a linear inverse problem had to be solved numerically, a procedure which is slow separately and iteratively. TV denoising problem can be and has the potential of getting stuck in a local minima. solved efficiently by several re cently developed numerical In this work, we develop an ecient and global minimization methods. While due to the nature of PPI the inverse prob- method for the binary level set representation of multi- lem can be ill-conditioned to a degree that increases with phase Chan-Vese model based on graph cuts. If the av- reduction factor in data acquisition. This makes the inver- erage intensity values of the dierent phases are suciently sion much more unstable and time consuming. To over- evenly distributed, the energy function becomes submod- come this difficulty an optimal first order gradient method ular. Otherwise, a novel method for minimizing nonsub- in the sense of complexity analysis developed by Nesterov modular functions is proposed with particular emphasis on is applied in our scheme. M oreover, a gridding preprocess, this energy function. We also show that non-local exten- that shifts the non-Cartesian data onto Cartesian grids, is sions of the multiphase Chan-Vese model can be globally used to avoid the inverse gridding in each iteration for fur- minimized by our method. ther reduction of computational time. Comparisons with various recently proposed methods indicate the outstand- Egil Bae ing efficiency of our algorithm with state-of-the-art recon- University of Bergen struction effects. [email protected]

Xiaojing Ye Xue-cheng Tai Department of Mathematics, University of Florida Dept. of Mathematics, University of Bergen, Norway and 358 Little Hall, Gainesville, FL32611-8105 Div. of Math. Sciences, Nanyang Tech. University xye@uﬂ.edu [email protected]

Yunmei Chen University of Florida MS8 [email protected]fl.edu Dual Norm Based Iterative Methods for Image Restoration Feng Huang Invivo Corporation, Philips HealthCare, Gainesville, FL Proximal point methods have been employed to stabilize [email protected] ill-posed problems in the last decades (see Osher et al., He et al.) which employ L2-quadratic and L1 data-fitting terms, respectively. Recently, Iusem-Resmerita proposed MS8 a proximal point method for minimizing a convex func- Variational Properties of a Functional for Multi- tion defined on a non-reflexive Banach space which is the phase Segmentation dual of another Banach space. Our aim here is to investigate, based on that method, several approaches to image We consider a functional for multiphase image segmen- restoration. tation which has been proposed by Sandberg, Kang and Chan. The functional is a modified version of the Mum- Miyoun Jung ford and Shah functional for the partition problem. In the Department of Mathematics new functional the length term of the Mumford and Shah UCLA functional is multiplied by the sum of the ratios perime- [email protected] ter/area of the sets of the partition. We prove the existence of minimizers for a weak version of the functional defined Elena Resmerita on the class of sets with finite perimeter. Then we study Industrial Mathematics Institute the regularity of boundaries of sets which constitute a weak Johannes Kepler University minimizer. Technical tools used in the proofs are adapted [email protected] from the analysis of the Mumford and Shah functional in the piecewise constant case. Luminita A. Vese University of California, Los Angeles Riccardo March Department of Mathematics Istituto per le Applicazioni del Calcolo, CNR [email protected] [email protected]

Sung Ha Kang MS8 Georgia Inst. of Technology Mean Curvature Based Image Denoising Mathematics [email protected] We propose a new variational model for image denoising, which employs mean curvature information of the image surface (x, f(x)) induced by the given image f :Ω→ R. 56 IS10 Abstracts

Besides eliminating noise and preserving edges of objects Poisson noise. This paper proposes a multilevel algorithm efficiently, our method can keep corners of objects and for efficiently solving this variational model. As expected grey-scale intensity contrasts of images, and also remove of a multilevel method, it delivers the same numerical so- the staircase effect. We apply the proposed model for the lution many orders of magnitude faster than the standard denoising of curves and plane images, and also compare single-level method of coordinate descent time-marching. the results with those by using the classical Rudin-Osher- Supporting numerical experiments on 2D gray scale images Fatemi model. are presented.

Wei Zhu Raymond H. Chan Mathematics, University of Alabama The Chinese Univ of Hong Kong [email protected] Department of Mathematics [email protected]

MS9 Ke Chen Imaging and Time Reversal in Scattering Environ- University of Liverpool ments Liverpool, UK [email protected] This minitutorial will provide an introduction to sensor array imaging in cluttered media. We will analyze how wave scattering by the inhomogeneities of the medium can af- MS10 fect the resolution and the signal-to-noise ratio in imaging Fast Bayesian Reconstruction For Fully-3D an object from far-ﬁeld measurements. We will show how Positron Emission Tomography novel image-enhancement techniques have been obtained using tools from statistics and wave propagation in ran- 3D Positron Emission Tomography is an ill-posed inverse dom media. We will clarify the relations between time problem that can be solved by penalized likelihood opti- reversal experiments, active sensor imaging using migra- mization, to account for both noise and object statistics. tion or backpropagation of the array data set, and passive However, solving such a large-scale, space-variant problem sensor imaging using cross correlations of ambient noise remains a computational challenge. Our contribution is a signals. new approximation of the Hessian of the Poisson likelihood, which yields a substantial acceleration of inexact Newton Josselin Garnier algorithms. It also facilitates the prior weights tuning to Universite Paris 7 produce a reconstructed image with uniform and isotropic [email protected] spatial resolution.

Xavier Rondeau MS10 IRCCYN, Nantes (FRANCE) Methods for Confocal Microscpic 3D Image CRAL, CNRS, Saint-Genis-Laval (FRANCE) Restoration [email protected] We propose methods for the iterative restoration of fluorescence Confocal Laser Scanning Microscope (CLSM) images Jérôme Idier which are degraded by both blur and Poisson noise. The IRCCYN restoration is obtained as the minimization of the sum of a Nantes, France data term (given by the Poisson distribution) and a prior xxx term, which is a TV prior term, or a complex wavelet L1 norm. We investigated two possibilities: a criterion written Claude Comtat in the image domain (analysis case) or in the wavelet do- CEA main (synthesis case) . Results will be shown on biological Orsay, France 3D images. xxx

Laure Blanc-F´eraud, Praveen Pankajakshan, Mikael Eric Thi´ebaut Carlavan, Josiane Zerubia CNRS INRIA Saint-Genis-Laval, France Sophia Antipolis, France xxx laure.blanc [email protected], xxx, xxx, xxx

Jean-Christophe Olivo-Marin MS10 Institut Pasteur, Paris, France Total Variation Processing of Images with Poisson xxx Statistics

This talk deals with denoising of density images with poor MS10 Poisson statistics. We propose total variation (TV) based Multilevel Algorithm for a Poisson Noise Removal regularization techniques adapted to the case of Poisson Model with Total-Variation Regularization data, which we derive from approximations of logarithmic a-posteriori probabilities. In order to guarantee sharp Many commonly used models for the fundamental image edges we avoid the smoothing of TV and use a dual ap- processing task of noise removal can deal with Gaussian proach for the numerical solution. We illustrate the feasi- white noise. However such Gaussian models are not eﬀec- bility of our approaches for the reconstructions of cardiac tive to restore images with Poisson noise, which is ubiqui- data in positron emission tomography. tous in certain applications. Recently Le-Chartrand-Asaki derived a new data-ﬁtting term in the variational model for Alex Sawatzky University of Muenster IS10 Abstracts 57

Muenster, Germany University of California [email protected] Department of Mathematics [email protected] Christoph Brune Institute for Computational and Applied Mathematics University of Muenster, Germany MS11 [email protected] Tensor-valued Image Processing Using Splitting Methods Jahn Mueller, Martin Burger Tensor-valued data have gained significant importance in University of Muenster recent years, e.g., in diffusion tensor magnetic resonance Muenster, Germany imaging. Our aim is to transfer successful variational tech- [email protected], [email protected] niques for the restoration of scalar-valued images to the tensor-valued setting. We propose an operator-based ap- MS11 proach which makes use of the trace norm of matrices. Furthermore, we combine different regularizers including Diffusion Generated Motion for Evolving Interfaces higher-order terms via the infimal convolution functional. in Imaging and Vision Interestingly, the alternating split Bregman or Douglas- I will describe a class of algorithms for generating a va- Rachford splitting method can be used to decouple these riety of geometric motions of curves in 2D and surfaces regularizers. This gives rise to an efficient minimization in 3D. These algorithms reduce the desired geometric mo- algorithm. tion to alternating two very simple operations for which Simon Setzer fast algorithms already exist: Convolution with a kernel, University of Mannheim and construction of the signed distance function to a set. [email protected] In particular, the resulting algorithms are unconditionally stable, allowing for arbitrarily large time steps constrained only by accuracy considerations. Applications include im- MS12 age segmentation and high order models in image inpaint- Patch-based Fluorescence Video-microscopy Image ing, as well as certain problems of materials science that Restoration involve multiphase flow. The noise represents one of the main limiting factor for Selim Esedoglu the spatial and temporal resolution of live fluorescence mi- Department of Mathematics croscopy. We present here an approach to reduce the noise University of Michigan level and improve the spatial resolution of the images. Fol- [email protected] lowing the work of Kindermann and Osher (2005), we propose to minimize a non-local patch-based functional to de- MS11 rive a point estimate. The performances of the estimator are then improved by adapting its parameters using a bias- A Multilevel Decomposition Method for Fast L1 variance trade-off criterion. Regularized Deconvolution Jerome Boulanger Abstract not available at time of publication. RICAM Linz Tom Goldstein [email protected] UCLA Department of Mathematics [email protected] Peter Elbau RICAM [email protected] MS11 A Nonlinear PDE-based Method for Sparse Decon- volution MS12 4D Image Reconstruction via Optimal Transport In this paper, we introduce a new nonlinear evolution partial differential equation for sparse deconvolution problems. We discuss models and efficient algorithms for 4D recon- We show that our PDE preserves the l1 norm while low- struction in photonic imaging. Standard reconstruction ering the measurement residual. More importantly the so- methods do not incorporate time dependent information or lution of the PDE becomes sparser asymptotically. There- kinetics. This can lead to deficient accuracy particularly at fore, it can be treated as a natural and helpful plug-in to object boundaries, e.g. at cardiac walls. We present joint some algorithms for l1 minimization problems, e.g. Breg- models combining Poisson-TV reconstruction and concepts man iterative methods introduced to sparse reconstruction of optimal transport (mass conservation). The numerical problems. realization is based on operator splitting techniques and Uzawa methods. Dynamic deconvolution and PET results Yu Mao illustrate the performance of the proposed methods. UCLA Department of Mathematics [email protected] Christoph Brune Institute for Computational and Applied Mathematics Bin Dong University of Muenster, Germany UCSD [email protected] [email protected]

Stanley J. Osher 58 IS10 Abstracts

MS12 MS13 Statistical Multi-scale Strategies for Inverse Prob- Fast High-Dimensional Data Clustering with Total lems Variation In this talk, we present a novel class of statistical multi- In this talk, I will introduce an algorithm for graph clus- resolution (SMR) estimators for statistical linear inverse tering. Graph clustering aims at grouping similar high- problems in Hilbert spaces. These SMR-estimators can be dimensional data s.a. images. The main problem of graph computed in a completely data-driven way. We discuss clustering is to minimize the cut of a graph. Popular cuts consistency and convergence rates results in a very general are the normalized cut of Shi-Malik (3000 citations) and setting. In particular, we consider deconvolution problems the Cheeger’s cut, which are NP-hard problems. We intro- in biophotonic imaging and show that our estimators can duce a continuous relaxation of the Cheeger’s cut problem be designed in order to control the trade-off between regu- and we show that the relaxation is actually equivalent to larization and fit-to-data in a locally-adaptive way. Exam- the original problem, which is not the case with the Shi- ples from fluorescence microscopy illustrate our approach. Malik’s relaxation. We also give an algorithm which is experimentally very efficient on some clustering benchmarks since the algorithm can cluster 10,000 high-dimensional Klaus Frick points in a few seconds. This is joint work with A. Szlam University of Göttingen (NYU), T.F. Chan, T. Goldstein, and S. Osher (UCLA) [email protected] Xavier Bresson UCLA MS12 Department of Mathematics Statistical Issues from Single-molecule Biophysics [email protected]

Recent advances in nanotechnology allow scientists for the first time to follow a biological process on a single molecule MS13 basis. These advances also raise many challenging sta- Convex Relaxation Methods for Multilabel Opti- tistical inference problems. First, on the single-molecule mization level, by the law of statistical and quantum mechanics, the dynamics/process of a biomolecule is stochastic. Sec- In my presentation, I will introduce convex relaxation ond, since the experiments focus on and study only a methods to solve minimal parition problems and related few molecules, the data in single-molecule experiments are multi-label optimization problems. In contrast to com- much noisier than those in the traditional ensemble exper- monly employed level set methods, the proposed algo- iments in that one cannot use the actions of thousands of rithms do not require an initialization. Moreover the solu- molecules to average out the noise. Third, inferring the un- tions are either globally optimal or within a per-instance derlying stochastic dynamics is usually complicated by the bound of the optimum. Furthermore I will present novel presence of latent processes. In this talk we will use the in- and provably convergent algorithms which allow to effi- ference of DNA hairpin kinetics to illustrate the statistical ciently compute minimizers of the convex problems by and probabilistic challenges in single-molecule biophysics, means of projected gradient descent /ascent strategies. and introduce a Bayesian data augmentation method to The class of functionals considered includes the piecewise address the inference difficulties. constant and piecewise smooth Mumford-Shah functional. Samuel Kou This is joint work with Thomas Pock and Antonin Cham- Dept of Statistics bolle. Harvard University [email protected] Daniel Cremers Department of Computer Science University of Bonn MS13 [email protected] Numerical Resolution of Variational Problems In- volving Geodesic Distances MS13 Various problems in imaging require to find metric that Using Mathematical Morphology to (Approxi- minimizes under some constraints the geodesic lengths be- mately) Solve the TVL1 Model tween points. In this talk, I will present the Subgradient Marching Algorithm that computes a sub-gradient of a dis- Since the seminal work by Rudin-Osher-Fatemi in 1992, cretized geodesic distance. It allows one to solve numer- total variation models have become very popular. For the icaly by projected sub-gradient descent variational prob- last 10 years, the understanding of the behavior of the to- lems involving geodesic distances. I will show application tal variation denoising models used in image processing to traffic congestion, landscape optimization and travel has dramatically improved, as a consequence of the works time tomography in seismic imaging. This is a joint work of W. K. Allard, G. Belletini, V. Caselles, A. Chambolle, with Fethallah Benmansour, Guillaume Carlier and Filippo S. Esedoglu, M. Novaga, and others... Using tools de- Santambrogio. veloped in these works, we will describe the geometrical behavior of the TVL1 model and its connection with the Fethallah Benmansour Cheeger problem. In the convex case, exact solutions of CEREMADE, Université Paris Dauphine the TVL1 problem are given by an opening followed by a [email protected] simple test over the ratio perimeter/area. Shapes remain or suddenly vanish depending on this test. This particu- Gabriel Peyré lar behavior has allowed us to design an efficient numerical Ceremade, Université Paris Dauphine scheme based on morphological operators to simulate the [email protected] TVL1 model. This work has been supported by the French ”Agence Nationale de la Recherche” (ANR), under grants IS10 Abstracts 59

NATIMAGES (ANR-08-EMER-009) ”Adaptivity for nat- speed of the algorithm on synthetic and real hybrid linear ural images and texture representations” and FREEDOM data. (ANR07-JCJC-0048-01),”Movies, restoration and missing data”. Arthur Szlam Department of Mathematics Vincent Duval NYU Telecom ParisTech [email protected] [email protected] MS14 MS14 Robust Recovery of Low-Rank Structure from Im- Image Processing with Higher-order Statistics on agery Data Grassmannians Principal component analysis is a fundamental operation We identify a subspace, i.e. a point on a Grassmannian, in computational data analysis, with myriad applications that best describes a collection of images by simultaneously ranging from web search to bioinformatics to computer vi- accounting for variation in cumulants of all orders. For sion and image analysis. However, its performance and comparison, PCA-based techniques (e.g. Eigenfaces and applicability in real scenarios are limited by a lack of ro- Fisherfaces) take into account only the second order cumu- bustness to outlying or corrupted observations. This prob- lant, i.e. covariance. While ICA-based techniques do use lem can be formally stated as one of recovering a low rank higher-order cumulants, they invariably make strong as- matrix from large but sparse corruption. In this talk, we sumptions on the higher-order cumulants (e.g. E[XYZ]=0). discuss recent progress on this problem. Recent theoretical We try to model such irreducible higher-order dependence results show that under fairly broad circumstances it can rather than assuming it is zero. A limited-memory quasi- be exactly and efficiently solved by convex programming. Newton method on Grassmannian is used to perform the We discuss fast and scalable solutions to this convex pro- requisite optimization. gram, via proximal gradient algorithms as well as duality. We then show how these new tools impact real imaging ap- Lek-Heng Lim plications, including automatic face recognition and optic University of California at Berkeley flow estimation from video. These applications show the [email protected] power of the tools, but also demand non-trivial extensions to nonlinear and manifold structure (e.g., due to transformations of domain). MS14 Multi-manifold Semi-supervised Learning John Wright Department of Electrical and Computer Engineering Semi-supervised learning on a single manifold has been the University of Illinois at Urbana-Champaign subject of intense study. I will discuss the setting of multi- [email protected] ple manifolds, in which it is assumed that the target function is smooth with respect to the geodesic distance on each manifold, and the manifolds can intersect or partly over- MS15 lap. I will discuss a semi-supervised learning algorithm Fast Algorithms for Large-scale Diffusion-type that separates different manifolds into decision sets, and Imaging Problems performs supervised learning within each set. Using a finite sample analysis, it is possible to quantify the potential In this work, we address a 2d tomography problem, where gain of using unlabeled data in this multi-manifold setting. we try to reconstruct the absorption coefficient of an ellip- I will also present a practical version of the algorithm that tic PDE from boundary measurements induced by a large involves a novel application of Hellinger distance and size- number of sources. We consider a square geometry where constrained spectral clustering. the light sources and measurements are located regularly on opposite sides of the domain. The problem in this form Aarti Singh requires solving a large nonlinear inverse problem, where Machine Learning Department the forward problem is given by multiple elliptic PDEs, Carnegie Mellon University and is thus computationally intensive. To address this, [email protected] we propose to solve a linearized version of the problem based on the Born approximation and show that substantial gains can be made in computation. By revealing the MS14 special structure of the problem, we design fast methods to Hybrid Linear Modeling by Multiscale Geometric assemble the coefficient matrix for the linearized problem. Analysis We also propose fast matrix-vector product routines that can be used to solve the linear system with iterative meth- The hybrid linear modeling problem is to identify a set of d- ods or sparse SVD. Finally we introduce a fast inversion dimensional affine sets in a D-dimensional Euclidean space. algorithm that produces the solution of the inverse problem It arises, for example, in object tracking and structure from by solving a sequence of small systems. We demonstrate motion. The hybrid linear model can be considered as the the effectiveness of our method with several examples. second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method Gunay Dogan for hybrid linear modeling based on selecting a set of local Mathematical and Computational Sciences Division best fit flats that minimize a global l1 error measure. The National Institute of Standards and Technology size of the local neighborhoods is determined automatically [email protected] using Jones’ l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and George Biros are found by our method. We give extensive experimental Georgia Institute of Technology evidence demonstrating the state of the art accuracy and 60 IS10 Abstracts

[email protected] across their corresponding contours. For the latter step we use a Newton method to solve the nonlinear optimality system. We use shape sensitivity calculus to find a de- MS15 scent direction for the cost functional with respect to the Regularizing Kaczmarz Iterations: Analysis and geometrical variable which leads to an update formula for Application to Photoacoustic Tomography the contours in the level-set framework. The identification of density and/or activity distributions from tomography We analyze regularizing Kaczmarz methods for solving sys- data is an ill-posed problem. After introducing a proper tems of linear ill-posed equations notion of convergence for the space of piecewise constant functions, we present results on the existence and conver- Aix = yi for i = 0,...,N − 1 , gence of minimizers for the Mumford-Shah like functional which use each of the equations separately. Here Ai are for linear operators. We present reconstructions from syn- operators between spaces X and Yi. We are mainly inter- thetic SPECT/CT data with different noise levels as well δ ested in the case where we have only noisy data yi ∈ Yi as regularization theory for the Mumford-Shah like method δ satisfying yi − yi≤δi with δi > 0 (noise levels). Numer- for linear operators. ical experiments are presented related to inverse problems in photoacoustic tomography. Esther Klann University of Linz, Austria Markus Haltmeier [email protected] Compational Science Center University of Vienna Ronny Ramlau [email protected] Johannes Kepler Universität Linz, Austria [email protected] Otmar Scherzer Computational Science Center Wolfgang Ring University Vienna Institut fuer Mathematik [email protected] Universitaet Graz [email protected] MS15 Multiphase Image Segmentation and Modulation MS16 Recovery Based on Shape and Topological Sensi- Model Based Compressive Imaging tivity Compressive sensing is an alternative to Shannon sampling Topological sensitivity analysis is performed for the piece- for acquisition of sparse or compressible signals that can wise constant Mumford-Shah functional. Topological and be well approximated by just K ¡¡ N elements from an N- shape derivatives are combined in order to derive an algo- dimensional basis. The standard CS theory dictates that rithm for image segmentation with fully automatized ini- robust signal recovery is possible from M = O(K log(N/K)) tialization. Segmentation of 2D and 3D data is presented. measurements. We demonstrate that it is possible to sub- Further, a generalized Mumford-Shah functional is pro- stantially decrease M without sacrificing robustness by posed and numerically investigated for the segmentation leveraging more realistic signal models that go beyond sim- of images modulated due to, e.g., coil sensitivities. ple sparsity by including dependencies between values and locations of the signal coefficients. Michael Hintermueller Humboldt-University of Berlin Richard G. Baraniuk [email protected] Rice University Electrical and Computer Engineering Department Antoine Laurain [email protected] Karl-Franzens University of Graz, Austria [email protected] MS16 A Fast Reconstruction Algorithm for Deterministic MS15 Compressive Sensing A Mumford-Shah Level-set Approach for Tomog- raphy Data - Reconstruction and Regularization We propose a deterministic compressed sensing matrix that comes by design with a very fast reconstruction algorithm, We deal with a level-set based approach for the simulta- in the sense that its complexity depends only on the num- neous reconstruction and segmentation of density and/or ber of measurements n and not on the signal dimension activity distributions from tomography data. SPECT/CT N. The matrix construction is based on the second order is a hybrid imaging technique enabling a direct correlation Reed-Muller codes. This matrix does not have RIP uni- of anatomical information (density distribution) from CT formly with respect to all k-sparse vectors, but it acts as a (Computerized Tomography) and functional information near isometry with very high probability. (activity distribution) from SPECT (Single Photon Emis- sion Computerized Tomography). We model activity and Robert Calderbank density distributions as piecewise constant functions. The Princeton University segmenting contours and the corresponding function val- [email protected] ues of both the activity and the density distribution are found simultaneously as minimizers of a Mumford-Shah like functional over the set of admissible contours and for fixed contours over the spaces of piecewise constant density and activity distributions which may be discontinuous IS10 Abstracts 61

MS16 Bayesian, variational, or shrinkage methods. We propose Compressive Sensing on Manifolds a specialized hybrid method combining the advantages of these approaches. The restored log-image minimizes a cri- Nonparametric Bayesian methods are employed to consti- terion combining L1 data-fidelity on the coefficients of a tute a mixture of low-rank Gaussians, for high dimensional hard-thresholded curvelet transform of the log-data and data constrained to a low-dimensional subregion. The TV regularization on the log-image. We derive a conver- number of mixture components and rank are inferred from gent fast scheme based on Douglas-Rachford splitting. The the data. The resulting algorithm can be used for learn- numerical results are promising. ing manifolds and reconstructing signals from manifolds, based on compressive sensing (CS) projection measure- Mila Nikolova ments. The statistical CS inversion is performed analyt- Centre de Mathématiques et de Leurs Applications ically. We derive the required number of CS measurements (CMLA) needed for successful reconstruction. ENS de Cachan, CNRS [email protected] Larry Carin Electrical & Computer Engineering Sylvain Durand Duke University Universite Rene Descartes [email protected] Paris, France xxx MS16 Jalal Fadili Sparse Learning via Iterative Minimization CNRS-ENSI-CAEN-Universite de Caen We present a regularized approach to sparse signal recov- Caen, France ery. Sparse Learning via Iterative Minimization, or SLIM, xxx follows an lq-norm constraint (for 0 ¡ q = 1), and can thus be used to provide increased sparsity compared to exist- MS17 ing l1-norm based approaches. We compare SLIM to several well-known sparse methods, including the widely-used Frame-based Proximal Algorithms for Poisson CoSaMP approach. Without significantly increasing com- Data Recovery putational cost, as compared to CoSaMP, we show that We consider convex optimization techniques for data re- SLIM provides superior performance for sparse signal recovery aiming at minimizing a criterion mixing a spatial covery applications. domain regularization (e.g. isotropic or anisotropic total Jian Li variation using various gradient filters), and a transform University of Florida domain regularization (e.g. a term promoting sparsity). [email protected]fl.edu An accelerated version of the Parallel ProXimal Algorithm (PPXA) is proposed that avoids to invert a large-size linear operator as required by some alternative numerical so- MS17 lutions, e.g. the split Bregman method. Non-Additive Noise Removal Using Variable Split- Caroline Chaux ting and Augmented Lagrangian Optimization UniversitéParis-Est We propose a new approach to handle non-additive noise [email protected] models (namely multiplicative and Poissonian) in image recovery problems. Our approach uses two main building Jean-Christophe Pesquet, Nelly Pustelnik blocks: variable splitting, yielding a constrained optimiza- UniversitéParis-Est tion problem; handling this optimization problem using an Marne la Vallée, France augmented Lagrangian method. We show that the result- xxx, xxx ing algorithms are instances of the alternating direction method of multipliers and that the conditions guarantee- ing its convergence are satisfied. Experiments show that MS17 our approach yields state-of-the-art performance. A Comparative Review of SAR Images Speckle De- noising Methods Based on Functional Minimiza- MarioA.T.Figueiredo tion Instituto de Telecomunicaões, Instituto Superior Técnico Lisboa,Portugal Synthetic aperture radar (SAR) as a coherent imaging mario.fi[email protected] modality leads to multiplicative speckle noise. We focus here on discrete MRF energy mimimization-based ap- Jose M. Bioucas-Dias proaches to filter speckle and on their continuous, varia- Instituto de Telecomunicacoes tional counterpart. Investigations proposed so far involve in particular: logarithm of the image, variational and aug- Instituto Superior Tecnico p q [email protected] mented Lagrangian methods, generalized L + L model and graph cuts (joint interferometric phase and amplitude image filtering). Those are compared on selected images MS17 with a common evaluation protocol. This work is funded by Multiplicative Noise Removal Using L1 Fidelity on French Defence Agency contract DGA REI 2008.34.00.42 Frame Coefficients Jean-Francois Aujol Classical multiplicative noise removal approaches use ei- CMLA, ENS Cachan, CNRS, UniverSud ther the raw data or its log transform and apply filtering, [email protected] 62 IS10 Abstracts

Emmanuel Bratsolis MR Imaging University of Athens, Department of Physics, Panepistimiopolis, GR-15784, Athens, Greece Parallel magnetic resonance imaging (pMRI) is a technique [email protected] which uses multiple receiver coils to speed up data acquisition time. Traditionally, down-sampling is applied in the Jerome Darbon ky-direction in frequency domain. The missing informa- CMLA CNRS UMR 8536 Ecole Normale Supérieure de tion is recovered from those parallel receiver coils, and an Cachan, unliasing inversion is needed for reconstruction. Here, we 61 avenue du président Wilson 94235 Cachan, France propose another parallel imaging technique. We scan only [email protected] a small region in the frequency domain while maintaining the same size of field-of-view. We acquire data from a sequence of receiver coils. Each gives a low-resolution Loic Denis ´ ´ image. The missing high-resolution image can be recov- Ecole Supérieure de Chimie Physique Electronique de ered from these low-resolution images due to the spatial Lyon and independence of the sensitivity functions of these receiver Laboratoire Hubert Curien, CNRS UMR 5516, coils. St-Etienne,´ France [email protected] I-Liang Chern Department of Mathematics Jean-Marie Nicolas, Xavier Rondeau National Taiwan University TELECOM ParisTech, Paris (France) [email protected] [email protected], [email protected] MS18 Marc Sigelle An Image Space Approach to Cartesian Based Par- TELECOM ParisTech, allel MR Imaging with Total Variation Regulariza- Paris (France) tion [email protected] The Cartesian parallel magnetic imaging problem is formulated variationally using a high order penalty for mod- Florence Tupin ulations and a total variation like penalty for the image. TELECOM ParisTech, Paris (France) Then the optimality system is derived and numerically dis- fl[email protected] cretized. The full problem is first considered in terms of the subproblems of modulation correction and aliasing correction. The cost functional used is non-convex, but the MS17 derivative of the cost has a bilinear residual term, and the Gamma and Poissonian Noise Removal functional is convex in each single argument. Thus, convex analysis is used to formulate the optimality condition for We consider a variational restoration model consisting of the image in terms of a primal-dual system. Also, a nonlin- the I-divergence as data fitting term and the total variation ear Gauss-Seidel iteration is used to minimize with respect semi-norm or nonlocal means as regularizer for removing to one variable after the other using Newton’s method. Fa- multiplicative Gamma noise. Although the I-divergence is vorable computational results are shown for artifical phan- the typical data fitting term when dealing with Poisson toms as well as for realistic magnetic resonance images. noise we substantiate why it is also appropriate for clean- ing Gamma noise. We propose to compute the minimizer Michael Hintermueller of our restoration functional by applying Douglas-Rachford Humboldt-University of Berlin splitting techniques, resp. alternating direction methods of [email protected] multipliers, combined with an efficient algorithm to solve the involved nonlinear systems of equations. We prove the Q-linear convergence of the latter algorithm. Finally, we MS18 demonstrate the performance of our whole scheme by nu- Human Brain Mapping using Computational Qua- merical examples. (The talk is considered as a possible siconformal Geometry ’fill-in-talk’.) In Human Brain Mapping, neuroscientists commonly aim Tanja Teuber to identify structural differences between healthy and un- University of Mannheim, Germany healthy brains, in order to detect systematic patterns of al- [email protected] terations in brain diseases. Surface-based cortical analysis is an important strategy and has found useful applications Simon Setzer in disease analysis. The main obstacle is that the human University of Mannheim brain cortical surface is a very complicated manifold with [email protected] difficult geometry. In this talk, I will describe how conformal and quasiconformal geometry can be used to analyze Gabriele Steidl brain surfaces accurately and systematically. I will firstly Institute of Mathematics und Computer Science describe how conformal and quasiconformal maps can be Universitaet Mannheim, Germany computed. These maps give the best global parameteriza- [email protected] tions of cortical surfaces which align landmarks and can be used for various applications such as surface registration, feature detection, computation on surfaces, etc. Secondly, MS18 different surfaces with landmarks correspondence have dif- High-resolution Image Reconstruction for Parallel ferent conformal structures. This gives ”signatures” for different brain surfaces for shape analysis. In the second IS10 Abstracts 63

part of my talk, I will describe how conformal structure of Hausdorff distance using mass transportation ideas. the brain surface can be used for shape analysis, using Te- ichmuller theory as a tool. Specifically, I will describe how Facundo Memoli different conformal modules can be computed and used for Stanford University, Mathematics Department abnormality detection in brain surfaces. [email protected]

Ronald LM Lui Department of Mathematics MS19 Harvard University Spectral Approaches to Shape Matching, Segmen- [email protected] tation and Statistical Shape Analysis Complex geometric objects have gained much importance MS18 in many different application fields such as medicine, com- Auto-Probing System for Breast Cancer Detection puter aided design or engineering. Modern sensor technolo- in Magnetic Resonance Imaging (MRI) gies produce large amounts of 3D (or higher dimensional) data, that need to be analyzed and processed automati- This project aims to develop a breast cancer detection sys- cally. Methods to compare, recognize and process shape tem with the invention of auto-probing methodology to (2D surfaces or 3D solid objects) are essential ingredients localize and visualize the region of cancerous lesion. This to achieve this goal. This talk will give an overview on dif- system can reduce the analysis time and enables more thor- ferent applications of spectral methods in shape analysis. I ough examination for breast screening. The lesion will be will demonstrate how the eigenvalues and eigenfunctions of coloured and exposed out on the MR images for better the Laplace-Beltrami operator yield powerful tools to de- identification and verification of the lesions characteristics. scribe and analyze shape. Due to their isometry invariance The region of interest selection enables the system to gener- they are optimally suited to deal with non-rigid shapes of- ate a graph which contains clearer details about the lesion. ten found in nature, such as a body in different postures. Furthermore, higher sensitivity and specificity is expected The normed beginning sequence of the spectrum can be to be achieved with this system in comparison to the cur- used as a global signature for shape matching and database rent practice where random probing is applied. retrieval, while the eigenfunctions and their topological analysis, employing the Morse-Smale complex, persistence Kok Swee Sim diagram or the Reeb graph, can be applied for shape regis- Centre of Multimedia Security and Signal Processing tration, segmentation and local shape analysis. Examples Multimedia University, Malaysia of applications such as database retrieval of near isometric [email protected] shapes, statistical shape analysis of subcortical structures and hierarchical segmentation of articulated shapes will be presented. MS19 Comparing Shape Properties by Multidimensional Martin Reuter Persistent Topology MIT-CSAIL [email protected] In this talk we shall briefly illustrate the use of multidimensional persistence for shape comparison. Moreover, we shall present some recent theoretical results that we MS19 have obtained about multidimensional persistent topology, Multiscale Signature Based on Heat Diffusion proving the stability of multidimensional persistent homol- ogy and showing how its discontinuities can be localized. We propose a novel point signature based on the properties of the heat diffusion process on a shape. Our signature, called the Heat Kernel signature (or HKS), is obtained by Patrizio Frosini restricting the well-known heat kernel to the temporal do- University of Bologna main. Remarkably we show that under certain mild as- Dipartimento di Matematica sumptions, HKS captures all of the information contained [email protected] in the heat kernel, and characterizes the shape up to isometry. This means that the restriction to the temporal domain, on the one hand, makes HKS much more concise and MS19 easily commensurable, while on the other hand, it preserves Metric Geometry in Shape Analysis all of the information about the intrinsic geometry of the shape. In addition, HKS inherits many useful properties The problem of object matching under invariances can be from the heat kernel, which means, in particular, that it is studied using certain tools from Metric Geometry. The stable under perturbations of the shape. Our signature also main idea is to regard objects as metric spaces (or measure provides a natural and efficiently computable multi-scale metric spaces). The type of invariance one wishes to have way to capture information about neighborhoods of a given in the matching is encoded in the choice of the metrics point, which can be extremely useful in many applications. with which we endow the objects. The standard example is To demonstrate the practical relevance of our signature, we matching objects in Euclidean space under rigid isometries: present several methods for non-rigid multi-scale matching in this situation one would endow the objects with the based on the HKS and use it to detect repeated structure Euclidean metric. More general scenarios are possible in within the same shape and across a collection of shapes. which the desired invariance cannot be reflected by the preservation of an ambient space metric. Several ideas due Jian Sun to M. Gromov are useful for approaching this problem. Stanford-CS In this talk we discuss different adaptations of these, and [email protected] in particular we construct an Lp version of the Gromov- Maks Ovsjanikov, Leonidas Guibas 64 IS10 Abstracts

Stanford University metric directly derives from the diffusion tensor. These [email protected], [email protected] tensors will be used to measure physical three-dimensional distances between different locations of a brain diffusion tensor image. The key concept is the notion of geodesic dis- MS20 tance that will allow us to find optimal paths in the white Image Compression with Anisotropic Geodesic Tri- matter. Such optimal paths are reasonable approximations angulations of neural fiber bundles. The geodesic distance function can be seen as the solution of two theoretically equivalent but, We propose to compress images using anisotropic Delau- in practice, significantly different problems in the partial nay triangulations generated from a Riemannian farthest differential equation framework: an initial value problem point seeding strategy. This seeding forces triangles to fol- which is intrinsically dynamic, and a boundary value prob- low sharp edges and directional features. The compression lem which is, on the contrary, intrinsically stationary. The is achieved by approximating images by linear splines over two approaches have very different properties which make the triangulations, and by coding both the spline coeffi- them more or less adequate for our problem and more or cients and the deviation of the anisotropic triangulations less computationally efficient. The dynamic formulation from the Euclidean Delaunay triangulation. The resulting is quite easy to implement but has several practical draw- encoder competes well, on geometric images, with wavelet- backs. On the contrary, the stationary formulation is much based encoders such as JPEG-2000. more tedious to implement; we will show, however, that it has many virtues which make it more suitable for our con- Sebastien Bougleux nectivity mapping problem. University of Caen GREYC CNRS Christophe Lenglet [email protected] Department of Electrical and Computer Engineering University of Minnesota Gabriel Peyre [email protected] CEREMADE, Universite Paris Dauphine [email protected] Emmanuel Prados INRIA Rh Laurent D. COHEN [email protected] CEREMADE, Universite Paris Dauphine and CNRS [email protected] Jean-Philippe Pons Centre Scientifique et Technique du Batiment [email protected] MS20 A Tubular Model for Orientation Dependent Vessel Rachid Deriche Segmentation Using Anisotropic Fast Marching Odyssée Lab, INRIA Sophia Antipolis We present a new interactive method for tubular structure [email protected] extraction, like vessels in 2D and 3D images. The basic tools are minimal paths solved using the fast marching al- Olivier Faugeras gorithm. Our method is based on a variant of the minimal INRIA path method that models the vessel as a centerline and [email protected] surface. The crucial step of our method is the definition of the local metrics to minimize. We have chosen to exploit the tubular structure of the vessels one wants to extract MS20 to built an anisotropic metric. The designed metric is well Restrictions of the Fast-marching-method for the oriented along the direction of the vessel, admits higher Anisotropic Eikonal Equation velocity on the centerline, and provides a good estimate of the vessel radius. Based on the optimally oriented flux this In many applications one wants to solve the anisotropic measure is required to be robust against the disturbance eikonal equation on a given cartesian grid. Using the introduced by noise or adjacent structures with intensity 8-point (or the 4-point) neighborhood discretisation one similar to the target vessel. looses the causality property of the update formulae if the anisotropy has certain properties. We discuss this situation Laurent D. Cohen and state cirteria to decide wether the discretization is suit- CNRS, UMR 7534 able for the given problem or not. Furthermore we present Universite Paris-Dauphine, CEREMADE a method which can deal in general with anisotropy. This [email protected] method uses virtual updates, analogue to the virtual updates on unstructured triangulations [James A. Sethian. Fethallah Benmansour Level set methods and fast marching methods. Evolv- CEREMADE, Université Paris Dauphine ing interfaces in computational geometry, fluid mechanics, [email protected] computer vision, and materials science. Cambridge Mono- graphs on Applied and Computational Mathematics, 1999] and it uses the same idea to handle anisotropy as it is MS20 done in [Folkmar Bornemann and Christian Rasch. Finite- Brain Connectivity Mapping Using Riemannian element discretization of static Hamilton-Jacobi equations Geometry, Control Theory and PDEs based on a local variational principle. Comput. Visual Sci., 9:57; 69, 2006]. We introduce an original approach for the mapping of the cerebral white matter connectivity from diffusion tensor Thomas Satzger imaging (DTI). Our method relies on a global modeling of Technische Universität München the acquired MRI volume as a Riemannian manifold whose [email protected] IS10 Abstracts 65

MS20 from image deblurring will be presented. Anisotropic Fast Marching in Pathophysiological Modeling Julianne Chung University of Maryland Bridging the gap between clinical applications and patho- [email protected] physiological models is one of the new challenges of medical image analysis. In this work, we propose an efficient Glenn Easley and accurate algorithm to solve anisotropic Eikonal equa- Systems Planning Corporation tions, in order to link mathematical models using reaction- [email protected] diffusion equations to sparse clinical observations, such as medical images. We use the proposed algorithm in two dif- Dianne P. O’Leary ferent modelling applications: tumour growth and cardiac University of Maryland, College Park electrophysiology. Department of Computer Science [email protected] Ender konukoglu INRIA Sophie Antipolis [email protected] MS21 Obtaining Better Images - Design in Imaging Maxime Sermesant, Phani Chinchapatnam, Nicholas Ayache Obtaining better images can be done by combining soft- INRIA ware and hardware. In this talk we present a general frame- [email protected], work that allows for designing better instrumentation and [email protected], reconstruction algorithms. We show that such framework [email protected] leads to a large scale stochastic optimization problem. We then suggest a few approaches for the solution of the problem. We show the effectiveness of our method using a few MS21 imaging methods such as limited angle tomography and FaIMS: A Fast Algorithm for the Inverse Medium super resolution Problem in Acoustic Scattering Eldad Haber We consider the inverse medium problem for the time- Department of Mathematics harmonic wave equation with broadband and multi-point The University of British Columbia illumination in the low frequency regime. Such a prob- [email protected] lem finds many applications in geosciences (e.g. ground penetrating radar), non-destructive evaluation (acoustics), and medicine (optical tomography). We use an integral- MS21 equation (Lippmann-Schwinger) formulation, which we Deblurring for Related Images Using Hybrid Reg- discretize using a quadrature method. We consider only ularization for Multiple Right Hand Systems small perturbations (Born approximation). To solve this inverse problem, we use a least-squares formulation. Image deblurring is ill-posed, even for blur described by a We present a new fast algorithm for the efficient so- spatially invariant linear operator. In this talk we focus lution of this particular least-squares problem. If Nf on deblurring of large scale problems using Tikhonov regis the number of excitation frequencies, Ns the number ularization applied at the local level as part of a domain of the different source locations of the point illumina- decomposition algorithm. The global iterative approach tions, Nd the number of detectors, and N the discretiza- requires that solutions are obtained of the subproblem sys- tion size for the scatterer, a dense singular value de- tem for multiple right hand sides, where each right hand composition for the overall input-output map will have side depends on the current global iterative solution. The 2 [min(NsNf Nd,N)] ×max(NsNf Nd,N) cost. We have de- algorithm is made more efficient by using updating of the veloped a fast SVD-based preconditioner that brings the initial local Krylov subspaces per problem with minimal cost down to O(NsNf NdN) thus, providing orders of mag- restarts. Our numerical results illustrate the feasibility of nitude improvements over a black-box dense SVD or an the approach. unpreconditioned linear iterative solver. Rosemary A. Renaut George Biros, Stephanie Chaillat Arizona State University Georgia Institute of Technology School of Mathematical and Statistical Sciences [email protected], [email protected] [email protected]

Youzuo Lin MS21 Arizona State University Regularization in a Multichannel Framework for [email protected] Problems Arising in Image Processing Applications

Ill-posed inverse problems arise in a variety of significant MS22 applications in image processing, and efficient regulariza- Variational Photometric Stereo tion methods are needed to compute meaningful solutions. The algorithms for image reconstruction that are discussed It is well-known that photometric stereo data provides lo- here are based on transforming an image into some fre- cal information surface normals and the depth data must quency domain and incorporating regularized inversion and subsequently be reconsidered via an integration process. wavelet filtering methods within a multichannel framework. In this talk, we shall discuss ways to combine the use of Numerical algorithms for the choice of the regularization local data and surface integration into a single depth from and filtering parameters will be discussed, and examples 66 IS10 Abstracts

photometric stereo variational functional. Div. of Math. Sciences, Nanyang Tech. University [email protected] Alfred M. Bruckstein Computer Science Department Eiji Sugisaki, Jie Qiu, Lei Jia, Hock Soon Seah Technion IIT, Haifa, Israel School of Computer Engineering [email protected] Nanyang Technological University [email protected], [email protected], [email protected], MS22 [email protected] Multigrid Narrow Band Surface Reconstruction via Level Set Functions MS22 In this talk I will discuss a new method for implicit surface Augmented Largrangian Method, Dual Methods reconstruction from unorganized point clouds. Our algo- and Split Bregman Iteration for ROF, Vectorial TV rithm employs a multigrid solver on a narrow band, which and High Order Models greatly improves the computational efficiency of surface re- In this talk, the augmented Lagrangian method is applied construction process. The new model can reconstruct sur- to overcome the non-differentiability and to make fast nu- faces from noisy unorganized point clouds that also have merical schemes of the ROF model. We observe close con- missing information. Comparing to traditional methods, nections between the method proposed here and some of our method is significantly faster and the reconstructed the existing methods, such as the dual method of CGM surfaces have detailed information. and Chambolle, split Bregman iteration, and splitting and Bin Dong penalty based method. Moreover, our method are easily UCSD extended to vectorial TV and high order models. [email protected] Chunlin Wu School of Physical and Mathematical Sciences Jian Ye Nanyang Technological University Mathematics, UCLA [email protected] [email protected] Xue-cheng Tai Igor Yanovsky Dept. of Mathematics, University of Bergen, Norway and Jet Propulsion Laboratory, California Institute of Div. of Math. Sciences, Nanyang Tech. University Technolog [email protected] [email protected]

Rima Gandlin MS23 Department of Mathematics Microlocal Analysis of the Geometric Separation Carnegie Mellon University Problem [email protected] Images are often composed of two or more geometri- Achi Brandt cally distinct constituents; in neurobiological imaging, for UCLA instance, point-structures (spines) and curve-structures [email protected] (dendrites) are mixed. We will present a theoretical analysis showing that accurate geometric separation of point and curve singularities can be achieved by minimizing Stanley J. Osher the 1-norm or thresholding the coefficients of a wavelet- University of California curvelet/shearlet-dictionary. Driving our analysis is the Department of Mathematics clustered sparsity of the ideal coefficients in microlocal [email protected] phase space. Gitta Kutyniok MS22 University of Osnabrueck Surface Reconstruction and Shading from Sparse [email protected] Gradient Fields Based on Vector Inpainting We propose vector inpainting methods for reconstructing David L. Donoho a surface from given strokes which usually make a shape of Stanford University object to look like 3D surface. After initial vectors are as- Department of Statistics signed on the stokes, the vectors are distributed via a func- [email protected] tional minimization with the incompressibility constraint which is the alternative condition of forcing the integrabil- MS23 ity condition in typical surface reconstruction. We apply the proposed method to generate anime-like shading. Characterization of Singularities and Edge Detec- tion using the Continuous Shearlet Transform Jooyoung Hahn Division of Mathematical Sciences Directional multiscale systems such as the Shearlet Trans- Nayang Technological University form were recently introduced to overcome the limitations [email protected] of the traditional wavelet transform in dealing with multidimensional data. In fact, while the continuous wavelet transform is able to identify the location of singularities of Xue-cheng Tai functions and distributions through its asymptotic behav- Dept. of Mathematics, University of Bergen, Norway and ior at fine scale, it lacks the ability to capture the geometry IS10 Abstracts 67

of the singularity set. In this talk, we show that the Shear- transforms used in collaborative filtering, with particular let Transform has the ability to precisely characterize both emphasis on the geometrical adaptation and on the learn- the location and orientation of the set of singularities of 2D ing of basis elements from noisy data. and 3D functions. This is relevant in imaging applications such as edge detection and feature extraction. Alessandro Foi Department of Signal Processing Demetrio Labate Tampere University of Technology, Finland University of Houston alessandro.foi@tut.fi [email protected] Vladimir Katkovnik, Karen Egiazarian Tampere University of Technology MS23 vladimir.katkovnik@tut.fi, karen.egiazarian@tut.fi Microlocal Analysis and Travel Time Tomography

We consider the problem of determining the anisotropic MS24 index of refraction of a medium by measuring the travel Another Role for Sparsity in Pattern Matching: A times of waves going through the medium. We consider Simple, First-principle Derivation Based on Com- both the case of transmission tomography and reflection putational Complexity tomography. We consider pattern matching problems where a pattern Gunther Uhlmann library, a set consisting of a large number of vectors, is University of Washington to be queried for the presence of user-provided patterns [email protected] in a Neyman-Pearson setting. Without any constraints on computational complexity, it is clear that one can an- MS23 swer such queries with arbitrarily high accuracy. Establish- ing computational complexity as the fundamental resource Doppler Synthetic Aperture Hitchhiker Imaging that needs to be traded with matching accuracy, our ap- In this talk, we consider passive airborne receivers that use proach formulates the search problem as the maximization backscattered signals from sources of opportunity trans- of accuracy for a given constraint in computational com- mitting fixed-frequency waveforms. Due to its combined plexity. In effect, our work represents the pattern library in passive synthetic aperture and the fixedfrequency nature terms of its computational-complexity-dependent approx- of the transmitted waveforms, we refer to the system under imations, where coarser approximations are computation- consideration as Doppler Synthetic Aperture Hitchhiker ally easier to search but lead to less accurate results. Our (DSAH). We present a novel image formation method for solutions naturally lead to sparse approximations, estab- DSAH. Our method first correlates the windowed signal ob- lishing a duality between sparse decompositions and pat- tained from one receiver with the windowed, filtered, scaled tern matching problems: (a) Patterns that are easy to find and translated version of the received signal from another must be sparse in some domain, (b) with low computa- receiver. This processing removes the transmitter related tional complexity, one can only hope to reliably find sparse variables from the phase of the Fourier integral operator approximations of patterns. that maps the radiance of the scene to the correlated sig- Onur Guleryuz nal. We, next, use the microlocal analysis to reconstruct DoCoMo Communications Laboratories USA the scene radiance by the weighted-backprojection of the [email protected] correlated signal. The image reconstruction method is applicable with both cooperative and non-cooperative sources of opportunity using one or more airborne receivers. It has MS24 the desirable property of preserving the visible edges of Local and Non-local Similarity for Visual Recogni- the scene radiance. Additionally, it is an analytic recon- tion From a Single Example struction technique which can be made computationally efficient. We present numerical simulations to demonstrate We present a novel framework for detection/recognition of the performance of the image reconstruction method and visual (2-D and 3-D) objects without training. The pro- to verify the theoretical results. posed framework operates using one example (query) of an object of interest to find similar matches; does not require Birsen Yazici prior knowledge (learning) about objects being sought; and Department of Electrical, Computer and Systems does not require any pre-processing step or segmentation Engineering of a target image/video. Our method is based on the com- Rensselaer Polytechnic Institute putation of local regression kernels as descriptors from a [email protected] query, which measure the likeness of a pixel, voxel, or patch, to its surroundings. State of the art performance MS24 is demonstrated on challenging datasets in several visual processing tasks including generic detection and recogni- Non-local Filtering of Images Using Data-driven tion of visual objects in 2-D and actions in 3-D, in diverse Transforms contexts and under varying imaging conditions. In addi- We consider the so-called grouping and collaborative filter- tion, using the patch-based framework, we are able to ro- ing approach: similar patches in an image or video are col- bustly and accurately capture visually salient objects and lected and jointly transformed using a higher-dimensional their boundaries, closely mimicking human fixation data in transform, sparsity is then enforced by shrinkage of the both static and dynamic scenes. higher-dimensional spectrum. This approach has proved Hae Jong Seo, Peyman Milanfar to be very successful, especially as the core element of de- EE Department noising, deblurring, and other inverse filtering algorithms. University of California, Santa Cruz We discuss various aspects related to the adaptivity of the 68 IS10 Abstracts

[email protected], [email protected] tions to color filtering. IEEE Transactions on Image Pro- cessing, 5(11):1582-1586, 1996; Wei Zhu and T. F. Chan. Image denoising using mean curvature. Preprint available MS24 from http://www.math.nyu.edu/∼wzhu/]. For instance, Universal Sparse Modeling it is known that TV models (and variants including graph cuts based models) suffer from staircasing effect in image The goal of this talk is to make formal connections between denoising and fail to deliver a visually satisfactory recon- sparse modeling and information theory, and in particular, struction in many situations in image inpainting where im- universal coding and MDL. We will show how this leads ages cannot be assumed to be piecewise constants. Further, to novel sparsity-inducing priors which have a number of the same arguments carry over to the vector-valued mod- advantages over more classical l0 and l1 ones. Joint work els. High order models, on the contrary, do not present with I. Ramirez and F. Lecumberry. staircasing in image denoising, and allow large distance reconnection and smooth recovery of missing parts in im- Guillermo Sapiro age inpainting. In this work we first propose and analyze University of Minnesota two high order and curvature-based denoising models for Dept Electrical & Computer Engineering vector-valued images which allow stronger coupling among [email protected] different channels than a channel-by-channel approach for a given noisy vector-valued image u0 ⎧ ⎫ MS25 ⎨ m ⎬ Analytic Sensing: A New Approach to Source λ 0 2 min Φ(κ) dx + |u − u | dx Imaging and Its Application to EEG u1,...,um ⎩ 2 ⎭ Ω =1 Ω Electroencephalography (EEG) provides us with a non- ⎧ ⎫ invasive way to access information about the brain’s cor- ⎨ m ⎬ λ 0 2 tical activity. Mapping back the electrical potential mea- min Φ(κ) dx + |u − u | dx u1,...,um ⎩ 2 ⎭ sured on the scalp to the underlying source configuration Ω =1 Ω is known as ”source imaging”. To render the problem well- n m posed, additional constraints on the solution are needed. where u =Ω⊂ R → R i.e., u =(u1,...,um)withu = Specifically, we use a parametric source model (sum of u(x1,...,xn) ∀ =1,...,m, dx =(dx1,...,dxm), κ dipoles) and we propose a new framework termed ”ana- the curvature of th image channel and Φ a given function. lytic sensing,” that lead to a non-iterative technique for Then a fast multigrid algorithm for the numerical solution multi-dipole fitting. The key contribution is to apply ana- is developed and tested. Advantages over TV based and lytic test functions that ”sense” the influence of the source other coupling models are illustrated. Finally extension distribution around virtual sensors. The choice of these of these techniques to color image inpainting is considered sensors allows us to estimate the dipoles’ positions by find- and some preliminary results are reported. ing an annihilation filter similar to ”finite rate of innovation” techniques. We show how to apply analytic sensing to Carlos Brito 3D and to EEG in particular. Preliminary results demon- University of Liverpool, UK strate the technique’s potential to retrieve multiple dipoles [email protected] at once, a problem that is difficult to solve by (numerical) least-squares fitting due to the many local minima. Joint Ke Chen work with: D. Kandaswamy, D. Van De Ville University of Liverpool [email protected] Thierry Blu Department of Electronic Engineering The Chinese University of Hong Kong MS25 [email protected] Iterative Methods for Image Reconstruction and Applications to Bioluminescence Tomography Djano Kandaswamy, Dimitri Van De Ville Biomedical Imaging Group Iterative methods for image reconstruction have become Ecole Polytechnique Federale de Lausanne very popular today for imaging research and applications. djano.kandaswamy@epfl.ch, dimitri.vandeville@epfl.ch The Landweber method and EM algorithm are widely used methods for image reconstruction. I will first introduce the Landweber method and the EM algorithm. Then I MS25 will report our progress about bioluminescence tomography High Order Vector-valued Models for Image (BLT). BLT is an emerging molecular imaging technique Restoration in the form of an ill-posed inverse source problem subject to Cauchy data of the diffusion equation. Variational techniques for gray-scale image restoration have been deeply investigated for many years, however, Ming Jiang little research has been done for the vector-valued case School of Mathematical Sciences and the very few existent works are total-variation-based Peking University models [P. Blomgren and T.F. Chan. Color TV: to- [email protected] tal variation methods for restoration of vector-valued images. IEEE Transactions on Image Processing, 7(3):304- 309,1998; X. Bresson and T.F. Chan. Fast dual mini- MS25 mization of the vectorial total variation norm and appli- Source Reconstruction for Spectrally-resolved Bi- cations to color image processing. Inverse Problems and oluminescence Tomography with Sparse A priori Imaging, 2(4):455-484, 2008; G. Sapiro and D.L. Ringach. Information Anisotropic diffusion of multivalued images with applica- We develop a new tomographic algorithm for spectrally- IS10 Abstracts 69

resolved bioluminescence tomography. This method uses Telecom Paris the nature of the source sparsity to improve the reconstruc- [email protected] tion quality with a regularization implementation. Based on verification of the inverse crime, the proposed algorithm is validated with Monte Carlo-based synthetic data and MS26 the popular Tikhonov regulariz ion method. Testing with Multiscale Image Representation Using a Novel different noise levels and single/multiple source settings at Integro-differential Equations different depths demonstrates the improved performance of this algorithm. Experimental reconstruction with a mouse- We propose a novel integro-differential equation (IDE) for shaped phantom further shows the potential of the pro- a multiscale image representation. To this end, one inte- posed algorithm. grates in inverse scale space a succession of refined ‘slices’ of the image, which are balanced by a typical curvature Xiaoqun Zhang term at the finer scale. The original motivation came University of California Los Angeles. from a variational-based hierarchical decomposition of im- [email protected] ages. We then use standard techniques from PDE-based image processing - filtering, edge preserving and tangen- tial smoothing, to yield a family of modified IDE models MS26 with applications to image denoising and deblurring prob- Regularizing with Anisotropic Total Variation lems. The IDE models depend on a user scaling function which is shown to dictate the BV properties of the residual Total variation regularization has been used for image de- error. Numerical experiments demonstrate applications of noising for about twenty years now. These regularizations our new IDE approach. have other uses as well; in particular, they can be used to detect differences in scales in data. I have been study- Eitan Tadmor ing the geometric and regularity properties of minimizers University of Maryland for the associated variational problems with the goal of USA better understanding them. In this talk I will describe [email protected] some new results in this area. Some of these results describe minimizers where total variation is defined using an Prashant Athava anisotropic norm for the gradient; the motivation for this Department of Mathematics work, which is joint with Kevin Vixie, is that some compu- University of Maryland tational schemes for computing minimizers naturally use a [email protected] polygonal approximation to the standard Euclidean metric to define total variation. MS26 William Allard Image Restoration Using One-dimensional Profiles Duke University of Sobolev Norms for Noise and Texture Department of Mathematics [email protected] We propose a variational model for image denoising and deblurring, using total variation and Sobolev norms of neg- Kevin R. Vixie ative degree of differentiability. The unknown image is re- Washington State University covered as the sum of two components, cartoon and tex- [email protected] ture. We impose prior information on the texture and on the noise, by learning one-dimensional profiles of Sobolev norms of textures and noise components. These profiles MS26 assign to each negative exponent, the Sobolev norm of the Calibrable Sets and Scales for TV-L2 and TV-L1 texture or of the noise. Experimental results for joint de- Models blurring and denoising are shown.

In this talk, we address the problem of scale definition, Yunho Kim based on the notion of calibrable set. In a first part, we Department of Mathematics, UCI explain how the TV-L2 model can be used to define the [email protected] scale of an object. In a second part, we consider the TV- L1 model, and we show how this functional discriminates John B. Garnett between structure and texture according to the previous Department of Mathematics, UCLA definition of scale. This work has been supported by the [email protected] French ”Agence Nationale de la Recherche” (ANR), under grants NATIMAGES (ANR-08-EMER-009) ”Adaptiv- Luminita A. Vese ity for natural images and texture representations” and University of California, Los Angeles FREEDOM (ANR07-JCJC-0048-01),”Movies, restoration Department of Mathematics and missing data”. [email protected] Jean-Francois Aujol CMLA, ENS Cachan, CNRS, UniverSud MS27 [email protected] New Theory and Algorithms for Nonsmooth, Non- convex Minimization Vincent Duval Telecom Paris Tech In recent years, nonsmooth, nonconvex minimization has [email protected] become essential in image restoration. In this talk, we discuss some new algorithms for solving nonsmooth, noncon- Yann Gousseau vex optimization. Moreover, we present a lower bound the- 70 IS10 Abstracts

ory for the absolute value of nonzero entries in every local MS27 minimizer of an objective function composed of a quadratic Convex Relaxations of Metrics for Imaging with data-fidelity term and a nonconvex, non-Lipschitz regular- Missing Data ization term. This theory can be used to eliminate zero entries precisely in any numerical solution. Furthermore, The usual presentation of missing data/compressive sens- it clearly shows the relationship between the sparsity of ing problems is to consider the function ·0 as the limit the solution and the choice of the regularization parame- of the p-metrics as p 0. The problem with p<1is ters, so that the lower bound theory can be used for se- that the metric is nonconvex and convergence results for lecting desired model parameters. We also develop error numerical algorithms based on this are difficult at the very bounds for verifying the accuracy of numerical minimiz- least. We present an alternative approach based on regu- ers. To demonstrate applications of our theory, we pro- larization of the Fenchel conjugates of these metrics. We pose an orthogonal matching pursuit-smoothing conjugate propose solving gradient (OMP-SCG) hybrid method for solving the non- convex, non-Lipschitz minimization problem. Computa- tional results show the effectiveness of the lower bounds min Iϕ∗ (x) such that Ax = b (1) for identifying nonzero entries in numerical solutions and x∈Rn ,L the OMP-SCG method for finding a high quality numerical solution. ∗ ϕ∗ Xiaojun Chen where I ,L (x)isanentropy with integrand ϕ,L and relax- Department of Applied Mathematics ation parameters and L that corresponds to a symmetric The Hong Kong Polytechnic University scaled Fermi-Dirac entropy. This is a smooth convex re- [email protected] laxation of the conventional p optimization for 0 ≤ p ≤ 1 and amenable to rigorous analysis and efficient algorithms. MS27 Lower Semi-Continuity of Non-Local Functionals Russell Luke Dept of Mathematics, University of Delaware We recall a few of the recent non-local methods used Newark, Delaware 19716 in imaging analysis such as the non-local mean filter [email protected] and the derivative-free formulation of the total variation functional. Such non-local methods for filtering images have proven to handle especially repetitive MS28 structures as for instance textures much better than Joint Manifolds for Data Fusion classical PDE-based approaches. Trying to formulate these methods as energy minimisation problems, we The emergence of low-cost sensing architectures for diverse typically end up with energy functionals of the form modalities has made it possible to deploy camera networks J { § † § † ( )= X X ( , , ( ), ( ))dxdy on some Lebesgue that capture a single event from a large number of van- spaces. We give a criterion for these energy functionals tage points and using multiple modalities. In many sce- to possess a minimising point. The crucial part thereby is narios, these networks acquire large amounts of very high- the weak sequential lower semi-continuity of the function- dimensional data. Even a relatively small network of cam- als which essentially reduces to the separate convexity of eras can generate massive amounts of high-dimensional im- the function f in the last two variables. age and video data. One way to cope with such a data deluge is to develop low-dimensional data models. Mani- Peter Elbau fold models provide a particularly powerful theoretical and RICAM algorithmic framework for capturing the structure of data [email protected] governed by a low-dimensional set of parameters, as is often the case in a sensor network. However, these models do not typically take into account dependencies among MS27 multiple sensors. We thus propose a new joint manifold Sparse Regularization with Non-convex Regular- framework for data ensembles that exploits such depen- ization Terms dencies. We show that joint manifold structure can lead to improved performance for a variety of signal process- We consider the stable solution of ill-posed operator equa- ing algorithms for applications including classification and tions by means of non-convex Tikhonov regularization, manifold learning. Additionally, recent results concerning where the regularization term acts separately on the co- random projections of manifolds enable us to formulate a efficients of an expansion with respect to a given basis, for network-scalable dimensionality reduction scheme that ef- instance a Fourier or wavelet basis. We discuss conditions ficiently fuses the data from all sensors. that guarantee that such an approach yields a well-posed regularization method. In addition, we derive a linear con- Richard G. Baraniuk vergence rate under the assumption of infinitely fast growth Rice University at zero, a condition that can only be satisfied with non- Electrical and Computer Engineering Department convex regularization terms. [email protected] Markus Grasmair Mark Davenport, Chinmay Hedge Computational Science Center Rice University University of Vienna, Austria [email protected], [email protected] [email protected] Marco F. Duarte Princeton University [email protected] IS10 Abstracts 71

MS28 dimensional space to a lower-dimensional space while ap- Distilled Sensing for Imaging proximately preserving some geometric properties. By op- erating with the compact representation of the data, it With the recent emergence of sparsity-exploiting technolo- is theoretically possible to produce approximate solutions gies (as in compressive sensing), a renewed emphasis has to certain large problems very efficiently. Recently, it has been placed on techniques that make judicious use of sam- been observed that dimension reduction has powerful appli- pling resources. In particular, adaptive sampling tech- cations in numerical linear algebra and numerical analysis. niques, where the sampling process is allowed to adapt or This talk provides a high-level introduction to randomized focus as a function of measurements previously obtained, methods for computing standard matrix approximations, are promising approaches for mitigating the effects of ad- and it summarizes a new analysis that offers (nearly) op- ditive noise in sparse recovery problems. In this talk I will timal bounds on the performance of these methods. In discuss our recent work on Distilled Sensing (DS), which practice, the techniques are so effective that they compete quantifies the surprising and dramatic improvements that with—or even outperform—classical algorithms. Since ma- are achievable using adaptivity. For example, we show that trix approximations play a ubiquitous role in areas rang- adaptivity enables the reliable recovery (detection and esti- ing from information processing to scientific computing, mation) of sparse signals in prohibitively-low SNR regimes it seems certain that randomized algorithms will eventu- where the best methods based on non-adaptive sampling ally supplant the standard methods in some application fail. In the context of imaging, DS can lead to significant domains. improvements in estimation accuracy. Joel Tropp Rob Nowak Applied and Computational Mathematics Department of Electrical and Computer Engineering Caltech University of Wisconsin-Madison [email protected] [email protected]

Jarvis Haupt MS29 Rice University Exploiting the Structure of Regularizers for Rapid [email protected] Solution of Euler-Lagrange Equations in Varia- tional Image Registration

Rui Castro Variational image registration techniques combine image Columbia University similarity measures with regularization terms in order to [email protected] guarantee that the resulting functional minimization problem is well-posed. In practice, typical regularization terms MS28 are quadratic differential forms that can be either spatially homogeneous or adaptive. In this talk, we describe two Compressive Sensing and Underwater Acoustics different rapid computing paradigms for estimating the so- We will discuss the application of the theory of compressive lution to the Euler-Lagrange equations resulting from var- sensing to two problems encountered in acoustics: source ious families of regularizers; one paradigm uses Fourier se- localization/tracking and communication over an uncertain ries solutions of the discretized Euler-Lagrange equations; channel. For the first problem, we show how a randomized the second employs convolution with a discretized Gaussian group testing can significantly reduce the number of acous- kernel to mimic the Green’s function solution to coupled tic simulations needed to locate and then track a source. PDE systems related to the Euler-Lagrange equations. For the second problem, we treat the scenario of communi- Nathan D. Cahill cating over an unknown channel as a blind deconvolution School of Mathematical Sciences problem, and show that if the (unknown) channel is sparse Rochester Institute of Technology and a random encoding scheme with a small amount of [email protected] redundancy is used by the source, then the receiver can discover both the message and the channel response by solving a well-posed optimization program. MS29 Justin Romberg A PDE Approach to Coupled Super-Resolution School of ECE with Non-Parametric Motion Georgia Tech The problem of recovering a high-resolution image from a [email protected] set of distorted low-resolution images is known as super- resolution. Accurate motion estimation among the low- William Mantzel, Salman Asif, Karim Sabra resolution measurements is a fundamental challenge of the Georgia Institute of Technology super-resolution problem. Some recent advances in this [email protected], [email protected], area have been focused on coupling the super-resolution [email protected] reconstruction and the motion estimation. However, the existing approach is limited to parametric motion models. We will address the coupled super-resolution problem MS28 with a non-parametric motion model in a variational for- Finding Structure with Randomness: Stochastic mulation. A PDE-approach will be proposed to yield a Algorithms for Constructing Low-rank Matrix De- numerical scheme. compositions Mehran Ebrahimi Computer scientists have long known that randomness can Dept. of Medical Biophysics be used to improve the performance of algorithms. A fa- University of Toronto miliar application is the process of dimension reduction, [email protected] in which a random map transports data from a high- 72 IS10 Abstracts

MS29 [email protected] Numerical Optimization for Constrained Image Registration Michael Bronstein EE Dept. Technion Israel Image registration is a technique to establish meaningful [email protected] correspondences between points in different scenes. It is an inevitable tool for various applications in medicine, geo- Ron Kimmel science, and other disciplines. However, obtaining reason- Technion, Haifa, Israel able deformations is a complex task. For example, many [email protected] applications require that the transformation is locally in- vertible, or even harder, keeps volumes changes within a reasonable bandwidth. In this work, solutions to the regis- MS31 tration problem are obtained by directly imposing a volume Exemplar-based Inpainting from a Variational constraint on each voxel in a discretized domain. The focus Point of View is on the development of an efficient and robust numerical algorithm and in particular, the study of an Augmented La- Among all methods for reconstructing missing regions in grangian method with a multigrid as preconditioned. We a digital image, the so-called exemplar-based algorithms demonstrate that this combination yields an almost opti- are very efficient and often produce striking results. They mal solver (i.e. linear time) for the problem. are based on the simple idea – initially used for texture synthesis – that the unknown part of an image can be Raya Horesh reconstructed by simply copying samples extracted from Emory University the known part. Many variants have been proposed whose Atlanta, GA performances vary according to the type of image. Be- [email protected] yond heuristic considerations, very little has been done in the literature to explain the performances of this class of Eldad Haber algorithms from a theoretical point of view. With a par- Department of Mathematics ticular focus on the ability to reconstruct the geometry, The University of British Columbia we discuss in this paper a variational interpretation in RN [email protected] of these methods. We propose an optimization model and several variants, and prove the existence of minimizers in the framework of functions of bounded variation. Focus- MS29 ing on a simple 2D situation, we provide experimental ev- Accelerating Non-Rigid Image Registration on idences that these global variational models are more effi- Gpus cient than a basic patch-based algorithm for reconstructing certain long-range geometric features without any loss of Non-rigid image registration tries to find a suitable defor- quality for the texture reconstruction. We eventually pro- mation field between two images that map one image into pose additional variants that fulfill a couple of axiomatic the other. This is widely used in medical imaging applica- requirements and have a better asymptotic behaviour as tions. Here, it is important to have fast image registration the patch size goes to zero. This is a joint work with Si- algorithms, e.g. in order to reduce the waiting time for the mon Masnou and Said Ladjal. This work has been done patient or to be able to register images during a surgery. with the support of the French “Agence Nationale de la We show how compute intensive parts of the image regis- Recherche” (ANR) under grant Freedom (ANR07-JCJC- tration algorithm can be parallelized and ported to GPUs 0048-01). and how the GPU code can be coupled to the FAIR (Flex- ible Algorithms for Image Registration) software package. Jean-Francois Aujol CMLA, ENS Cachan, CNRS, UniverSud [email protected] Harald Koestler University of Erlangen-Nuremberg [email protected] Sa¨ıd Ladjal Telecom ParisTech [email protected] MS30 Numerical Geometry of Non-Rigid Shapes Simon Masnou UniversitéParis6 Non-rigid shapes are ubiquitous in the world surrounding [email protected] us, at all levels from micro to macro. The need to study such shapes and model their behavior arises in the fields of computer vision, pattern recognition, and graphics in a MS31 wide spectrum of applications ranging from medical imag- MRI Superresolution Using High Resolution ing to security. The tutorial is a self-contained compre- Anatomical Priors hensive introduction to analysis and synthesis of non-rigid shapes, with a good balance between theory, numeric meth- In Magnetic Resonance Imaging low-resolution images are ods, and applications. One of the main emphases will be routinely interpolated to decrease voxel size and improve on practical methods. Examples of applications from com- apparent resolution. However, classical interpolation tech- puter vision and pattern recognition, computer graphics, niques are not able to recover the high frequency informa- and geometry processing will be shown. tion lost during the acquisition process. In the present paper a new superresolution method is proposed to recover Alex Bronstein such information using coplanar high resolution images. Department of Computer Science The proposed methodology takes benefit from the fact that Technion - Israel Institute of Technology in typical clinical settings both high and low-resolution im- IS10 Abstracts 73

ages of different types are taken from the same subject. MS31 These available high resolution images can be used to im- Modeling Locally Parellel Textures prove effectively the resolution of other coplanar lower resolution images. Experiments on synthetic and real data In this talk I will present a new adaptive framework for are supplied to show the effectiveness of the proposed ap- locally parallel texture modeling. Oscillating patterns are proach. A comparison with classical interpolation tech- modeled with functionals that constrain the local Fourier niques is presented to demonstrate the improved perfor- decomposition of the texture. We introduce a first convex mance of the proposed methodology over previous State- texture functional which is a weighted Hilbert norm. The of-the-art methods. weights on the local Fourier atoms are optimized to match the local orientation and frequency of the texture. This Antoni Buades adaptive convex model is then used to solve inverse prob- Paris Descartes lems in image processing, such as image decomposition and [email protected] inpainting. The local texture orientation and frequency of the texture component are adaptively estimated during the minimization process. Furthermore, in the inpainting case, MS31 convex models present the issue of attenuation inside large Image Denoising with Nonlocal Spectral Graph missing parts. The amplitude of the reconstructed oscil- Wavelets lating patterns tends indeed to vanish inside large holes. To deal with this difficult problem, a non convex general- We present a new method for denoising photographic im- ization of our model is designed. This new model enables ages based on a novel nonlocal spectral graph wavelet to impose the amplitude of the oscillating patterns inside transform. We employ the transform formed using the the reconstructed parts and to cope with the inpainting of graph Laplacian corresponding to a nonlocal image graph general oscillations profiles. Numerical results show that measuring similarities between image regions, yielding our method improves state of the art algorithms for direc- wavelets at multiple scales with the interesting property tional textures. This is a joint work with Pierre Maurel that they diffuse among regions of similar image content. and Jean-Francois Aujol. Denoising by soft thresholding with threshold determined from a simple Laplacian model for the clean coefficients Gabriel Peyré yields good results. Ceremade, Université Paris Dauphine [email protected] David Hammond EPFL david.hammond@epfl.ch Pierre Maurel IRISA [email protected] Karthik Raoaroor Ecole Polytechnique Federale de Lausanne karthik.raoaroor@epfl.ch Jean-Fan¸cois Aujol CMLA, ENS de Cachan [email protected] Laurent Jacques Université Catholique de Louvain [email protected] MS32 Scales Coming from K-functionals Pierre Vandergheynst Ecole Polytechnique Federale de Lausanne In image decomposition, an image f is decomposed into pierre.vandergheynst@epfl.ch u+v, where u and v are in some function spaces X and Y respectively. This can be seen as viewing f to belong to an interpolating space between X and Y. Given the choices MS31 for X and Y, we will discuss and analyze the choice for this Neighborhod Filters and Novel Bayesian Approxi- interpolating space, which provides us with an automatic mations for Non-local Image Regularization decomposition of f.

In this talk, I will present formal connections between Triet Le non-parametric estimation approaches, neighborhood fil- Department of Mathematics, Yale University ters and block estimators in the Bayesian framework. I [email protected] will provide a statistical interpretation to current patch- based methods and justify the Bayesian inference that needs to explicitly accounts for discrepancies between the MS32 model and the data. I will present a recent method recom- Edge-enhanced Image Reconstruction Using Total mended in situations where the posterior or the likelihood Variation Norm and High-order Edge-preserving are intractable or too prohibitive to calculate. In particu- Up-sampling Operators lar, the proposed approximations are suited for the analysis of large-dimensional distribution of patches and enable We have introduced an image resolution enhancement to denoise images corrupted by non-Gaussian noises. We method for multidimensional images based on a variational demonstrate our algorithms on both artificial and real ex- approach that uses the total variation norm as regulariz- amples. ing functional. Given an appropriate down-sampling operator, the reconstruction problem is posed using a decon- Charles Kervrann volution model under the assumption of Gaussian noise. INRIA Rennes - Bretagne Atlantique / MIA - INRA In this research work we explore different edge-preserving Rennes, France up-sampling operators with different orders of spatial ac- [email protected] curacy. The operators are defined using nonlinear local functions to preserve edges automatically when they are 74 IS10 Abstracts

present. We analyze the behavior and robustness of those problem. The iteration functions are constructed as a non- operators under noisy data. Numerical results are pre- linear convex combination of neighboring values allowing sented using those operators in conjunction with our vari- the solution to satisfy a maximum principle. We propose ational model for image enhancement. a speciﬁc stopping criterion that allows convergence in a ﬁnite number of iterations. We present numerical exam- Antonio Marquina ples of two-dimensional denoising and deblurring-denoising University of Valencia, Spain problems. [email protected] Suzana Serna Shantanu Joshi Deparment of Mathematics, UCLA LONI, UCLA [email protected] [email protected] Antonio Marquina Stanley J. Osher University of Valencia, Spain Mathematics, UCLA [email protected] [email protected] Stanley J. Osher Ivo D. Dinov University of California UCLA Department of Mathematics Center for Computational Biology [email protected] [email protected] MS33 Jack Van Horn LONI, UCLA Convex Formulation and Exact Global Solutions [email protected] for Multi-phase Piecewise Constant Mumford- Shah Image Segmentation

MS32 Most variational models for multi-phase image segmentation are non-convex and possess multiple local minima, Fast TV based Segmentation and Surface Interpo- which makes solving for a global solution an extremely diffi- lation cult task. In this work, we provide a method for computing Variational globally convex segmentation results involving a global solution for the (non-convex) multi-phase piece- total variation minimization have been devised in recent wise constant Mumford-Shah (spatially continuous Potts) years by Chan, Esedoglu and Nikolova, for segmentation image segmentation problem. Our approach is based on and by Chambolle for geometric motion. These can be used using a specific representation of the problem due to Lie et for classical geometric problems in vision, however they al. We then establish an augmented Lagrangian method were believed to be slow to implement. Recently developed to reduce the problem to a sequence of non-convex mini- fast algorithms involving Bregman methods turn out to be mization problems, each of which can globally solved using very effective for these problems. We’ll descibe progress in a convexification technique due to Pock et al. Unlike some this area. recent methods in this direction, our method can guarantee that a global solution is obtained. We believe our method Tom Goldstein to be the first in the literature that can make this claim. Mathematics, UCLA tagoldst at math.ucla.edu Ethan Brown Department of Mathematics University of California at Los Angeles Xavier Bresson [email protected] UCLA Department of Mathematics [email protected] Tony Chan University of California. Los Angeles [email protected] Jian Ye Mathematics, UCLA [email protected] Xavier Bresson UCLA Department of Mathematics Stanley J. Osher [email protected] University of California Department of Mathematics [email protected] MS33 Local Scales in Images

MS32 We propose a linear approach to extract local scales of Nonlinear Iterative Algorithms for Total Variation oscillatory patterns in images in a multi-scale fashion. We Denoising and Deblurring will discuss the relation of local scales to the theory of function spaces and the extension to nontangential local We propose nonlinear Jacobi and Gauss-Seidel iterative scales and non-linear evolution equations. procedures for approximating the solution of the Euler- Lagrange equations associated to the TV minimization Peter Jones denoising and deblurring problems. The algorithms are Yale University formulated from a suitable discretization of the Euler- [email protected] Lagrange equation associated to the speciﬁc variational IS10 Abstracts 75

Triet Le which involves and balances derivatives up to a certain or- Department of Mathematics, Yale University der. Applied to mathematical imaging, it usually leads to [email protected] nonsmooth and nonconvex minimization problems. Their numerical solution is discussed and examples are presented, showing in particular the absence of staircasing effects for MS33 this approach. A Variational Model for Infinite Perimeter Seg- mentations Based on Lipschitz Level Set Func- Kristian Bredies tions: Denoising While Keeping Finely Oscillatory Universität Graz Boundaries Institute of Mathematics and Scientific Computing [email protected] We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the Chan-Vese model, where the length penalization of the MS34 boundaries is replaced by the area of their neighborhood of DC Programming Approaches for Image Restora- thickness . Our aim is to keep fine details and irregular- tion and Image Segmentation ities of the boundaries while denoising additive Gaussian noise. For the numerical computation we revisit the classi- We present an efficient approach in nonconvex nonsmooth cal BV level set formulation considering suitable Lipschitz programming called DC (Difference of Convex functions) level set functions instead of BV ones. programming and DC algorithms (DCA) for two classes of problems in image processing: the image restoration Marcello Ponsiglione by globally minimizing the Gibbs energy function via a Dipartimento di Matematica Markov random field model, and the image segmentation Universita‘diRomaI via Fuzzy C-Means (FCM) clustering model. Experimental [email protected] results on noisy images have illustrated the effectiveness of the proposed algorithm and its superiority with respect to Marco Barchiesi the standard GNC algorithm (for image restoration) and BCAM, Bizkaia Technology Park, Building 500, 48160 FCM algorithm (for image segmentation). Derio, Sp [email protected] Hoai An Le Thi Université Paul Verlaine, Reims, France [email protected] Sung Ha Kang Georgia Inst. of Technology Mathematics MS34 [email protected] DC (Difference of Convex functions) Programming and DCA (DC Algorithms) for Smooth/ Nons- Triet M. Le mooth Nonconvex Programming Yale University [email protected] The DC programming and DCA address the problem of minimizing a function f = g−h ,(g, h being lower semicon- Massimiliano Morini tinuous proper convex functions on the Euclidean space) on SISSA a closed convex set. The DCA, based on local optimality Trieste,Italy conditions and DC duality, has been successfully applied [email protected] to a lot of different and various smooth/nonsmooth non- convex programs. Moreover it has quite often given global solutions and proved to be more robust and more efficient MS33 than related standard methods, especially in the large-scale Adapted Local Scales and Smoothness, and NL- setting. means Tao Pham Dinh The NL-means algorithm and its cousins represent a gray- Laboratory of Modeling, Optimization and Operations scale image not as a function of R2, but as a function of Research the set of patches of the image. On this set of patches, National Institute for Applied Sciences -Rouen, France the algorithm simply becomes a linear diffusion, with the [email protected] standard associated scale space. I will discuss why this point of view is useful and give examples from image and audio analysis. MS34 Linear Convergence Method for a Non-convex Arthur Szlam Variational Model Department of Mathematics NYU In this talk, we consider a non-convex variational model. [email protected] We propose to use strictly convex optimization models to approximate the non-convex functional. We show that the solutions of these strictly convex optimization models will MS34 converge to the global minimizer of the original non-convex Optimization with Total Generalized Variation functional. We show that the solution of the strictly convex Penalty optimization model can be determined by using an iterative algorithm, and the convergence rate is linear. Numer- In the talk, we focus on the solution of minimization prob- ical examples are presented to show the efficiency of the lems involving a total generalized variation penalty term. Total generalized variation is a novel nonsmooth concept 76 IS10 Abstracts

proposed method. MS35 Passive Imaging Using Distributed Apertures in Tieyong Zeng Multi-path Environments Department of Mathematics Hong Kong Baptist University We present a new passive image formation method capable [email protected] of exploiting information about multi-path scattering in the environment using measurements from a sparse array of Michael Ng receivers that rely on illumination sources of opportunity. Hong Kong Baptist University We use a statistical and physics-based approach to model Department of Mathematics multi-path propagation and formulate the imaging problem [email protected] as a spatially resolved binary hypothesis testing problem. Our imaging method is applicable in the presence of both cooperative and non-cooperative sources of opportunity. MS35 Synthetic Aperture Radar Imaging with Motion Birsen Yazici Estimation and Autofocus Department of Electrical, Computer and Systems Engineering We introduce from first principles a synthetic aperture Rensselaer Polytechnic Institute radar (SAR) imaging and motion estimation method [email protected] that is combined with radar platform trajectory estimation. This method segments the data into properly cali- brated small apertures and uses space-time phase methods MS36 (Wigner transforms and ambiguity functions) to estimate Statistical Methods for Manifold Learning target motion and trajectory perturbations. X-band persistent surveillance SAR is a specific application that is It has recently been recognized that if the signal of interest covered by our analysis. This is joint work with Thomas to an inverse problem is known to reside on a manifold, Callaghan and George Papanicolaou. the number of required measurements needed for accurate inference may be reduced substantially. This is closely re- Liliana Borcea lated to the new field of compressive sensing (CS). In this Rice University talk we discuss development of new nonparametric statis- Dept Computational & Appl Math tical methods to learn the statistical properties of a low- [email protected] dimensional manifold. We show how this technique may be employed in several applications, including CS. MS35 Lawrence Carin Transmission Eigenvalues and Their Application in Duke University Inverse Scattering Theory Dept of Electrical & Computer Engineering [email protected] We consider the scattering problem for an inhomogeneous medium and discuss a new related eigenvalue problem known as the interior transmission eigenvalue problem. We MS36 first prove that there exists a countable set of transmis- Bayesian Hypermodels in Medical Imaging sion eigenvalues and then show that these eigenvalues can be determined from the far field data. Finally, we obtain In this talk, we review the hierarchical Bayesian models in Faber-Krahn type inequalities for transmission eigenvalues medical applications. In the literature, it has been demon- which, if D is known, provide lower and upper bounds on strated in the context of machine learning and in image the index of refraction n(x). processing that Bayesian hierarchical model provide a flexible framework for implementing a priori information such Fioralba Cakoni as sparsity of the image or its gradient, and the interest University of Delaware in compressed sensing has increased the need to work out [email protected] further the possibilities of hierarchical models. We discuss various medical imaging applications where the hierarchical models turn out to be useful and improve the quality MS35 of the reconstructions. Direct and Inverse Obstacle Scattering Over Rough Surfaces Erkki Somersalo, Daniela Calvetti Case Western Reserve University We develop a theory for direct obstacle scattering of ob- [email protected], [email protected] stacles over a rough surface. Using that theory, we address the inverse obstacle scattering problem in which measurements of the wave field are collected on a planar array MS36 over a spectrum of wavelengths. For applications in single Using Learning and Posterior Modeling to Segment molecule detection and characterization, we seek to recover Images the number and locations of the scatterers as well as each of their spectral properties. This talk proposes a direct posterior modeling methodology for segmenting images. The methodology provides a Arnold D. Kim canonical way of using machine-learning techniques, such University of California, Merced as kernel-based methods, in a level-set segmentation. One [email protected] advantage of this approach is that it is possible to learn to segment complex images, such as ultrasound images, which have significant spatial inhomogeneity. This talk will present the methodology as well experimental results IS10 Abstracts 77

of using the posterior modeling technique. a novel method for the pixel unmixing problem that yields sparse abundance vectors. Hemant Tagare Yale University John Greer [email protected] National Geospatial-Intelligence Agency [email protected] MS36 Expectation-Maximization Algorithm with Local MS37 Adaptivity for Image Analysis Unsupervised Clustering of High Dimensional Sub- spaces In this work we develop an Expectation-Maximization (EM) algorithm with local adaptivity that can combine A clustering framework within the sparse modeling and global statistics, local statistics, and and geometric infor- dictionary learning setting is introduced in this work. We mation. In particular we apply our algorithm to image optimize for a set of dictionaries for which the signals are segmentation and classification. The key idea is to cou- best reconstructed in a sparse coding manner (subspaces). ple global statistics extracted from proper statistic model The proposed clustering uses a novel measurement for the with local statistical and geometrical information. These quality of the sparse representation. We illustrate state- combined information are used to design an adaptive local of-the-art results for supervised classification and unsuper- classification strategy that can both improve robustness vised clustering on standard standard datasets and texture and keep fine features. images. Hongkai Zhao Guillermo Sapiro University of California, Irvine University of Minnesota Department of Mathematics Dept Electrical & Computer Engineering [email protected] [email protected]

Shingyu Leung Hong Kong University of Science and Technology MS37 [email protected] Multiscale Representations for Point Cloud Data We shall describe a progressive encoder for Lidar point Gang Liang cloud data based on local PCA, adaptive partitioning, Industry Hausdorff distance, and implicit representation of the point [email protected] cloud surface. This encoder has as its goal best distortion in the Hausdorff metric for a given bit budget. Applica- Knut Solna tions of the encoder will be given for point cloud data. University of California at Irvine The encoder is designed to handle noisy data by utilizing [email protected] learning theory for the Hausdorff metric. Andrew Waters MS37 Rice University Pan Sharpening and Multimodal Data Fusion in [email protected] Remote Sensing Applications

There has been significant research on pan-sharpening mul- MS38 tispectral imagery with a high resolution image, but there Data Reduction Methods for Optical Tomography has been little work extending the procedure to high dimen- of Large DataSets sional hyperspectral imagery. We present a wavelet-based variational method for fusing a high resolution image and A current topic in Optical Tomography is the acquisition of a hyperspectral image with an arbitrary number of bands. data using camera detectors. The data can be obtained in To ensure that the fused image can be used for tasks such as a rotating scanning geometry and can include time resolved classification and detection, we explicitly enforce spectral data, leading to large 4 or 5 dimensional data sets of size coherence in the fusion process. This procedure produces up to 108 − 1010. Due to the inherent low resolution of images with both high spatial and spectral quality. We the method (stemming from its severe ill-posedness) much demonstrate this procedure on several AVIRIS and HY- of this data is redundant. In this talk we consider some DICE images. metohds for compressing the information content in these data sets and the commensurate improvement in image Andrea L. Bertozzi reconstruction performance. UCLA Department of Mathematics [email protected] Simon Arridge University College London [email protected] MS37 Dictionary Learning Methods for Hyperspectral Image Classification MS38 Approximation Errors and Model Reduction in 3D We investigate the application of sparse reconstruction and Diffuse Optical Tomography dictionary learning methods to hyperspectral image analysis. After training dictionaries for specific classes, we Model reduction is often required in diffuse optical tomog- classify unknown pixels by comparing reconstruction er- raphy (DOT), typically due to limited available computa- rors across the different class dictionaries. We also discuss tion time or computer memory. In practice, this means 78 IS10 Abstracts

that one is bound to use coarse mesh and truncated com- differences between (BV, L1) and (BV,L2) IDE schemes. putation domain in the model for the forward problem. In this talk we apply the Bayesian approximation error model Prashant Athavale for the compensation of modeling errors caused by domain IPAM, UCLA truncation and a coarse computation mesh in DOT. The [email protected] approach is tested using experimental data. The results show that when the approximation error model is em- Eitan Tadmor ployed, it is possible to use mesh densities and computation University of Maryland domains that would be unacceptable with a conventional USA measurement error model. [email protected] Ville P. Kolehmainen Department of Physics MS39 University of Kuopio Modeling Locally Parallel Oscillating Patterns Ville.Kolehmainen@uku.fi Since the seminal work by Y. Meyer in 2001, image decomposition into geometry + texture has drawn a lot of MS38 attention. In particular, it was shown by Osher-Sole-Vese, Optical Tomography with the Discontinuous and later by Aujol-Gilboa, that using a Hilbert space to Galerkin Method model texture is quite effective. In this work, we extend these ideas to build a spatially adaptive texture norm. Ex- We present a discontinuous Galerkin (DG) formulation of periments in image decomposition and in image inpaint- the diffusion equation to tackle the meshing issues asso- ing are shown to validate the approach. This work has ciated with finite element formulations. DG method has been supported by the French ”Agence Nationale de la also been employed to solve the diffusion equation on a Recherche” (ANR), under grant NATIMAGES (ANR-08- multi-layered highly diffusive domain with refractive index EMER-009) ”Adaptivity for natural images and texture mismatch between consecutive layers. Numerical studies representations”. are presented for the forward problem and reconstructions employing DG method on both experimental and simu- Jean-Francois Aujol lated data. These results show that DG formulations are CMLA, ENS Cachan, CNRS, UniverSud as accurate as finite element formulations and are better [email protected] equipped to tackle discontinuities in the solution. Pierre Maurel Surya Prerapa, Simon Arridge IRISA University College London [email protected] [email protected], [email protected] Gabriel Peyré MS38 Ceremade, Université Paris Dauphine Numerical Solutions of Inverse Transport Problems [email protected] with Interior Data for Imaging Applications

Inverse problems related to the linear radiative transport MS39 equation find applications in medical imaging such as op- Fast Gradient-Based Schemes for Total Variation tical tomography and optical molecular imaging. In tran- Minimization ditional optical tomography, the data used for imaging are only collected on the boundary of the imaging domain. We We present fast gradient-based schemes for image denoising consider in this talk some inverse transport problems where and deblurring problems based on the discretized total vari- we can collect interior data. We will present some numer- ation (TV) minimization model with constraints. Our ap- ical algorithms as well as some reconstructions with syn- proach relies on combining a novel monotone version of the thetic interior data. fast iterative shrinkage/ thresholding algorithm (FISTA) we recently introduced, with the well known dual approach Kui Ren to the denoising problem. We derive a fast algorithm for University of Texas the constrained TV-based image deblurring problem. The [email protected] proposed scheme is remarkably simple and is proven to exhibit a global rate of convergence which is significantly better than currently known gradient based methods. Our MS39 results are applicable to both the anisotropic and isotropic Integro Differential Equation Schemes Based on discretized TV functionals. Initial numerical results con- (BV, L1) Decomposition firm the predicted underlying theoretical convergence rate results, and demonstrate the viability and efficiency of the The hierarchical multiscale image representation of Tad- proposed algorithms on image deblurring problems with mor, Nezzar and Vese, gives rise to an integro-differential box constraints. This talk is based on a joint work with equation (IDE) for a multiscale image representation. One Marc Teboulle. can obtain a similar IDE using (BV,L1) multiscale hierarchical decomposition. To this end, one integrates in inverse Amir Beck scale space a succession of refined, recursive ‘slices’ of the Faculty of Industrial Engineering and Management image, which are balanced by a typical curvature term at TECHNION - Israel Institute of technology the finer scale. Once the IDE is obtained we can mod- [email protected] ify it based on our image processing needs. We will discuss various (BV, L1) IDE schemes incorporating filtering, edge enhancing and deblurring. We will also examine qualitative IS10 Abstracts 79

MS39 in search engines for efficient indexing and search of shapes. Inverse Free-discontinuity Problems and Iterative Thresholding Algorithms Alex Bronstein, Michael Bronstein Department of Computer Science Free-discontinuity problems describe situations where the Technion - Israel Institute of Technology solution of interest is defined by a function and a lower di- [email protected], [email protected] mensional set consisting of the discontinuities of the function. Hence, the derivative of the solution is assumed to be Maks Ovsjanikov, Leonidas Guibas a ”small function” almost everywhere except on sets where Stanford University it concentrates as a singular measure. This is the case, [email protected], [email protected] for instance, in certain digital image segmentation problems. 1) In presence of an inverse problem, no existence results were available so far. First of all we show prelimi- MS40 nary new results on the existence of minimizers for inverse Exploiting BoW Paradigm for 3D Shape Descrip- free-discontinuity problems, by restricting the solutions to tion and Matching a class of functions which we called the Rondi’s class. 2) If we discretize such situations for numerical purposes, the The Bag of Words (BoW) paradigm has been introduced inverse free-discontinuity problem in the discrete setting originally for natural language processing and it has been can be re-formulated as that of finding a derivative vector successfully applied in several other domains. For instance with small components at all but a few entries that ex- in Computer Vision the BoW approach has been proposed ceed a certain threshold. This problem is similar to those for object categorization, image retrieval and human action encountered in the field of ”sparse recovery”, where vec- recognition. Here, we show the effectiveness of the BoW tors with a small number of dominating components in onto the 3D domain by exploiting both i) region-based, and absolute value are recovered from a few given linear mea- ii) point-based techniques to characterize local parts of a surements via the minimization of related energy function- 3D shape. Region-based approaches build the visual vocab- als. As a second result, we show that the computation ulary starting from the regions extracted by a 3D object of global minimizers in the discrete setting is an NP-hard segmentation process. Point-based techniques are instead problem. 3) With the aim of formulating efficient com- oriented to the detection of few feature points from the 3D putational approaches in such a complicated situation, we surface. Moreover, we show how the spatial relations be- address iterative thresholding algorithms that intertwine tween object subparts can be easily encoded by combining gradient-type iterations with thresholding steps which were the BoW paradigm with shape context (i.e., local descrip- designed to recover sparse solutions. It is natural to wonder tors and global context). Several experiments are reported how such algorithms can be used towards solving discrete on different applications namely object retrieval and cate- free-discontinuity problems. This talk explores also this gorization, point-to-point matching, and 3D partial views connection, and, by establishing an iterative thresholding registration. algorithm for discrete inverse free-discontinuity problems, provides new insights on properties of minimizing solutions Umberto Castellani thereof. This is partially a joint work with Riccardo March University of Verona (CNR, Italy) and Rachel Ward (Courant Institute, NYU, [email protected] USA).

Massimo Fornasier MS40 Johann Radon Institute for Computational and Applied Geodesic Shape Retrieval with Optimal Transport Mathematics (RICAM) [email protected] In this talk, I will review several geodesic representations for shapes and surfaces, and their use for retrieval with invariance to bendings and articulations. I will present a new MS40 familly of high dimensional geodesic shape signatures, that ShapeGoogle: Geometric Words and Expressions extend several previous proposals. These new geodesic rep- for Invariant Shape Retrieval resentations take into account the interplay between several geodesic caracteristics. It is defined as high dimensional Large databases of 3D models available in public domain histograms of several key geodesic features, that detect have created the demand for shape search and retrieval al- global caracteristics of shapes and surfaces. The retrival gorithms capable of finding similar shapes in the same way is performed with a nearest neighbor query according to a search engine responds to text quires. Since many shapes the Wasserstein distance between these multi-dimensional manifest rich variability, shape retrieval is often required signatures. The search is performed with a fast approxi- to be invariant to different classes of transformations and mated optimal transport algorithm. This a joint work with shape variations. One of the most challenging settings in Julien Rabin and Laurent Cohen. the case of non-rigid shapes, in which the class of transformations may be very wide due to the capability of such Laurent D. Cohen shapes to bend and assume different forms. In this talk, we CNRS, UMR 7534 will apply modern methods in computer vision to problems Universite Paris-Dauphine, CEREMADE of non-rigid shape analysis. Feature-based representation [email protected] such as the Scale-Invariant Feature Transform (SIFT) and metric learning methods have recently gained popularity Gabriel Peyre in computer vision, while remaining largely unknown in Université Paris-Dauphine the shape analysis community. We will show analogous [email protected] approaches in the 3D world applied to the problem of non- rigid shape retrieval in large (potentially Internet-scale) Julien Rabin databases. This will allow us to adopt methods employed Telecom ParisTech [email protected] 80 IS10 Abstracts

MS40 [email protected] Surface Feature Detection and Description with Applications to Mesh Matching MS41 We revisit local feature detectors/descriptors developed for Image Registration and Segmentation Using a Non- 2D images and extend them to the more general frame- linear Elasticity Smoother work of scalar fields defined on 2D manifolds. We provide methods and tools to detect and describe features on sur- We present a new non-parametric faces equiped with scalar functions, such as photometric registration-segmentation method. The problem is cast as information. This is motivated by the growing need for an optimization one, combining a matching criterion based matching and tracking photometric surfaces over temporal on the active contour without edges for segmentation, and sequences, due to recent advancements in multiple cam- a nonlinear-elasticity-based smoother on the displacement era 3D reconstruction. We propose a 3D feature detector vector field. This modeling is twofold: first, registration is (MeshDOG) and a 3D feature descriptor (MeshHOG) for jointly performed with segmentation since guided by the uniformly triangulated meshes, invariant to changes in ro- segmentation process; it means that the algorithm pro- tation, translation, and scale. The descriptor is able to cap- duces both a smooth mapping between the two shapes and ture the local geometric and/or photometric properties in the segmentation of the object contained in the reference a succinct fashion. Moreover, the method is defined gener- image. Secondly, the use of a nonlinearelasticity-type reg- ically for any scalar function, e.g., local curvature. Results ularizer allows large deformations to occur, which makes with matching rigid and non-rigid meshes demonstrate the the model comparable in this point with the viscous fluid interest of the proposed framework. registration method. Several applications are proposed to demonstrate the potential of this method to both segmen- Radu Horaud tation of one single image and to registration between two INRIA Grenoble images. [email protected] Carole Le Guyader Andrei Zaharescu INSA Rouen, France Aimetis Inc [email protected] [email protected] Luminita A. Vese Edmond Boyer University of California, Los Angeles INRIA Grenoble Department of Mathematics [email protected] [email protected]

MS41 MS41 Elasticity in Image Registration Revisited Continuous Models for Rigid and Nonrigid Regis- tration We present a general hyperelasticity regularization framework for image registration. The framework is demon- We will present a robust continuous mutual information strated on a number of synthetic and real image registra- model for multimodality registration. The probability and tion applications. joint probability density functions for the continuous images are defined analytically. This model leads to a smooth Mads F. Hansen, Rasmus Larsen mutual information which does not have the typical inter- DTU Informatics polation artifacts, resulting in much higher success rates. [email protected], [email protected] Moreover, we will propose a nonrigid registration model formulated in a particle framework. Our model can accommodate both small and large deformations, with sharper MS41 edges and clearer texture achieved at less computational On Multiple Level-set Regularization Methods for cost. Numerical results on a variety of images are pre- Inverse Problems sented. We analyze a multiple level-set method for solving inverse Justin Wan problems with piecewise constant solutions. This method University of Waterloo corresponds to an iterated Tikhonov method for a particu- Department of Computer Science lar Tikhonov functional based on TV-H1 penalization. We [email protected] define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove con- Zhao Yi vergence and stability results of the proposed Tikhonov UCLA method. A multiple level-set algorithm is derived from [email protected] the first-order optimality conditions for the Tikhonov functional, similarly as the iterated Tikhonov method. The Lin Xu, Tiantian Bian proposed multiple level-set method is tested on an inverse University of Waterloo potential problem. Numerical experiments show that the [email protected], [email protected] method is able to recover multiple objects as well as multiple contrast levels. This is a joint work with A DeCezaro and A Leitão. MS42 Inverse Scattering by Compressed Sensing Xue-cheng Tai Dept. of Mathematics, University of Bergen, Norway and Inverse scattering problem is analyzed from the perspec- Div. of Math. Sciences, Nanyang Tech. University tive of compressed sensing. It is shown that with appro- IS10 Abstracts 81

priately designed bases and sampling methods the number dimensional denoising and three-dimensional TV denois- of measurements/sensors can be significantly reduced in ing. comparison to traditional methods. Frank Crosby Albert C. Fannjiang Naval Surface Warfare Center Department of Mathematics Panama City University of California at Davis [email protected] [email protected] Haomin Zhou Georgia Institute of Technology MS42 School of Mathematics Imaging Localized Scatterers with L1 Optimization [email protected] I will give a detailed comparison of resolution and robustness for array imaging with L1 and L2 optimization crite- MS43 ria, including results from numerical simulations. Joint L1 Visibility Optimization Using Variational Methods and L2 criteria will also be considered. This is work with Anwei Chai. Confined areas, such as those found in littoral regions, re- strict the maneuvering and sensing capabilities of Naval George C. Papanicolaou vessels. We introduce a solution to the confined area search Stanford University problem based on the calculus of variations which we im- Department of Mathematics plement using the level-set framework. The resulting algo- [email protected] rithm is completely autonomous and can be extended to account for: incomplete maps, sensor limitations (range, MS42 resolution, etc.), as well as other factors. We also introduce an algorithm for positioning n-sensors to achieve maximal Imaging and Detection in Cluttered Media coverage of a confined area.

We consider sensor imaging in a noisy environment by suit- Rostislav Goroshin ably migrating the cross correlations of the recorded sig- Naval Surface Warfare Center - Panama City nals. We analyze the properties of the imaging functional [email protected] in the high-frequency regime. We identify the scaling assumptions that allow us to image respectively, the support of random sources and smooth or rough medium variations. Haomin Zhou Georgia Institute of Technology School of Mathematics Knut Solna [email protected] University of California at Irvine [email protected] MS43 Crowd Counting: Modeling Abnormal Events for MS42 the Detection of Suicide Bombers Data Filtering for Coherent Array Imaging in Heavy Clutter We present some recent results on the problem of counting the number of people in a crowded scene. These results We consider the problem of coherent array imaging reflec- are obtained with a system for estimating the size of in- tors embedded in strongly scattering media. This problem homogeneous crowds, composed of pedestrians that travel appears in applications such as exploration geophysics and in different directions, without using explicit object seg- non-destructive testing of materials. Coherent imaging re- mentation or tracking. First, the crowd is segmented into sults in such media are not satisfactory because the coher- components of homogeneous motion, using the mixture of ent signal that arrives at the array is too weak. To extend dynamic textures motion model. Second, a set of simple the applicability range of coherent imaging techniques to holistic features is extracted from each segmented region, stronger scattering environments we propose to perform and the correspondence between features and the number appropriate filtering on the data prior to imaging. of people per segment is learned with Gaussian Process regression. We validate both the crowd segmentation the Chrysoula Tsogka crowd counting algorithms on hours of video. University of Crete and FORTH-IACM [email protected] Viral Bhalodia, Weixin Li, Nuno Vasconcelos UCSD [email protected], [email protected], [email protected] MS43 Total Variation Methods for 3D Lidar Image De- Truong Nguyen noising ECE, UCSD [email protected] New imaging capabilities have given rise to higher dimensional image processing. This paper presents a generalization of total variation (TV) based denoising model with MS43 specific application to three-dimensional flash lidar im- Object Classification and Identification from agery. The generalization uses a weighted norm, rather Acoustic Color Images than the standard Euclidean measure, that accounts for sampling differences that may exist along different axes. We introduce a method of enhancing a sonar image with We compare this new method against successive two- acoustic color. Our method emphasizes the discrimina- 82 IS10 Abstracts

tive properties of the returned spectrum for the purpose of Using Higher-Order Edge Detectors object discrimination. This is achieved by analyzing the discriminating power of different frequency bands and as- A novel approach is presented that allows the detection sociating the appropriate ones with a color map. of edges in piece wise smooth signals from partial Fourier data. Detection of edges has many important application Naoki Saito e.g. in medical image analysis or image reconstruction. University of California, Davis Our approach combines a method to find jump discontinu- [email protected] ities in Fourier data and ideas from compressed sensing. It is able to detect edges in Fourier data without the presence Quyen Huynh of ringing artifacts common to higher order edge detection Naval Surface Warfare Center, Panama City methods. [email protected] Wolfgang Stefan Rice University MS44 [email protected] Kronecker Compressive Sensing Aditya Viswanathan Compressive sensing (CS) is an emerging approach for ac- Arizona State University quisition of signals having a sparse or compressible repre- [email protected] sentation in some basis. While the CS literature has mostly focused on problems involving 1-D signals and 2-D images, Anne Gelb many important applications involve signals that are mul- Mathematics Department tidimensional; in this case, CS works best with represen- Arizona State University tations that encapsulate the structure of such signals in [email protected] every dimension. We propose the use of Kronecker product matrices in CS for two purposes. First, we can use Rosemary Renaut such matrices as sparsifying bases that jointly model the Arizona State University different types of structure present in the signal. Second, [email protected] the measurement matrices used in distributed measurement settings can be easily expressed as Kronecker product matrices. The Kronecker product formulation in these MS44 two settings enables the derivation of analytical bounds for Compressive Sensing via Iterative Support Detec- sparse approximation of multidimensional signals and CS tion recovery performance, as well as a means to evaluate novel distributed measurement schemes. We present a new compressive sensing reconstruction method “ISD’, aiming to achieve fast reconstruction and Marco F. Duarte a reduced requirement on the number of measurements Princeton University compared to the classical 1 minimization approach. ISD [email protected] addresses failed cases of 1–based construction due to insufficient measurements, in which the returned signals are Richard G. Baraniuk not equal or even close to the true signals. Specifically, Rice University given an incorrect signal, ISD detects an index set I that Electrical and Computer Engineering Department includes components most likely to be true nonzeros and [email protected] { | | } solves min i∈I xi : Ax = b for a new signal x,andit iterates these two steps alternatively using latest x and I MS44 from one another until convergence. Edge Guided Compressive Imaging Reconstruction Yilun Wang Cornell University Compressive imaging aims at reconstructing faithful im- [email protected] ages from a small number of measurements. We strive for sharper images from less measurements through efficiently using edge information. Accurate edge detection from un- Wotao Yin dersampled data is very challenging due to existence of Rice University ubiquitious artifacts and noise. Start with sampled data [email protected] with overwhelming small size, the proposed method is two folded: i) to detect edges from a not-so-perfect first round MS44 reconstruction; ii) to run an edge guided reconstruction. Effective Compressive Sensing with Toeplitz and Weihong Guo Circulant Matrices Department of Mathematics, Case Western Reserve University Compressive sensing requires a small number of incoher- [email protected] ent measurements of the unknown signal as the input. To achieve the co-incoherence, random linear projections are often among the best choices. However, they are difficult to Wotao Yin implement physically or the implementation would cause Rice University a prohibitive overhead. We describe how random Toeplitz [email protected] and circulant matrices can be easily (or even naturally) re- alized in various imaging applications and introduce fast MS44 algorithms for their corresponding signal reconstruction problems. Results show that they are not only as effec- Edge Detection in Blurred Data from Fourier Space IS10 Abstracts 83

tive as random matrices but also permit much faster signal The Technion, Israel reconstruction in one, two, and higher dimensions. [email protected]

Junfeng Yang Javier Turek Nanjing University Computer Science Department [email protected] Technion [email protected] Wotao Yin Rice University Irad Yavneh [email protected] Computer Science Department, Technion [email protected] Simon Morgan Los Alamos National Laboratory [email protected] MS45 Block Stein Sparse Denoising and Deconvolution Yin Zhang Rice University In this work, we propose fast image denoising and deconvo- Dept of Comp and Applied Math lution algorithms that use adaptive block thresholding in [email protected] sparse representation domain. Our main theoretical result investigates the minimax rates of Stein block thresholding in any dimension d over the so-called decomposition spaces. MS45 These smoothness spaces cover the classical case of Besov On Globally Optimal Local Modeling: From Mov- spaces for which wavelets are known to provide a sparse ing Least Square to Overparametrization representation, as well as smoothness spaces corresponding to the second generation curvelet-type construction. We This paper discusses a spectrum of methods for signal, shows that block estimator can achieve the optimal mini- curve, image and surface denoising, adaptive smoothing max rate, or is at least nearly minimax (up to a log factor) and reconstruction from noisy samples that involve lo- in the least favorable situation. The choice of the threshold cally modeling the data while performing local, semi- parameter is theoretically discussed and its optimal value local and/or global optimization. We show that the same is stated for the white Gaussian noise. We provide simple, methodolgy yields many of the previously proposed algo- fast and easy to implement algorithms. We also report a rithms, from the popular moving least squares methods comprehensive simulation study to support our theoreti- to the globally optimal overparametrization methods re- cal findings. The practical performance of our block Stein cently published for smoothing and optic-flow estimation. denoising and deconvolution algorithms compares very fa- However, the unified look at the spectrum of problems and vorably to state-of-the art algorithms on a large set of test methods also suggests a wealth of novel global functionals images. and local modeling possibilities. Jalal Fadili Alfred M. Bruckstein CNRS, ENSICAEN-Univ. of Caen, France Computer Science Department [email protected] Technion IIT, Haifa, Israel [email protected] MS45 3D Sparse Representations and Inverse Problems MS45 Image Super-Resolution using In this paper, we show that using a few three dimen- Sparse-Representation sional sparse transforms with atoms of different morphologies, including the wavelets and two types of curvelets, Scaling up a single image while preserving is sharpness we can design simple algorithms based on iterative thresh- and visual-quality is a difficult and highly ill-posed inverse oldings that solve many restoration and inverse problems problem. A series of algorithms have been proposed over such as denoising, morphological component separation, the years for its solution, with varying degrees of success. inpainting, de-interlacing or inverse Fourier/Radon trans- In CVPR 2008, Yang, Wright, Huang and Ma proposed form with relatively few projections. a solution to this problem based on sparse representation modeling and dictionary learning. In this talk I present Arnaud Woiselle,Jean-LucStarck a variant of their method with several important differ- Laboratoire AIM, CEA/DSM-CNRS-Universite Paris ences. In particular, the proposed algorithm does not need Diderot a separate training phase, as the dictionaries are learned CEA Saclay, DAPNIA/SEDI-SAP, Service directly from the image to be scaled-up. Furthermore, the d’Astrophysique high-resolution dictionary is learned differently, by forcing [email protected], [email protected] its alignment with the low-resolution one. We show the benefit these modifications bring in terms of simplicity of Jalal Fadili the overall algorithm, and its output quality. CNRS, ENSICAEN-Univ. of Caen, France [email protected] Michael Elad Computer Science Department Technion MS45 [email protected] Image Modeling and Enhancement via Structured Sparse Model Selection Matan Protter The CS depoartment Joint work with Guillermo Sapiro and Stéphane Mallat 84 IS10 Abstracts

An image representation framework based on structured sive sensing approach, which seem to be confusing. The sparse model selection is introduced in this work. The cor- mathematic exactness of an algorithm can be an irrelevant responding modeling dictionary is comprised of a family of metric for meaningfully evaluating the algorithms practical learned orthogonal bases. For an image patch, a model is utility in its practical applications. Discussion will thus be first selected from this dictionary through linear approxi- given as to how the performance evaluation of an algorithm mation in a best basis, and the signal estimation is then can be meaningfully carried out. calculated with the selected model. The model selection leads to a guaranteed near optimal denoising estimator. Xiaochuan Pan The degree of freedom in the model selection is equal to The University of Chicago the number of the bases, typically about 10 for natural im- Department of Radiology ages, and is significantly lower than with traditional over- [email protected] complete dictionary approaches, stabilizing√ √ the representation. For an image patch of size N × N, the compu- 2 MS46 tational complexity of the proposed framework is O(N ), typically 2 to 3 orders of magnitude faster than estima- Band-Restricted Estimation of Noise Variance in tion in an overcomplete dictionary. The orthogonal bases Filtered Backprojection Reconstructions from Re- are adapted to the image of interest and are computed peated CT Scans with a simple and fast procedure. State-of-the-art results We introduce a new estimator for noise variance in tomo- are shown in image denoising, deblurring, and inpainting. graphic images reconstructed using algorithms of the fil- Demo website: tered backprojection type. The new estimator operates on http://www.cmap.polytechnique.fr/ yu/research/SSMS/demo.html data acquired from repeated scans of the object under examination, is unbiased, and is shown to have significantly Guoshen Yu lower variance than the conventional unbiased estimator ECE, University of Minnesota for many scenarios of practical interest. We provide an ex- [email protected] tensive theoretical analysis of this estimator and present preliminary results with real x-ray computed tomography data. Guillermo Sapiro University of Minnesota Adam Wunderlich, Frederic Noo Dept Electrical & Computer Engineering Utah Center for Advanced Imaging Research [email protected] Department of Radiology, University of Utah [email protected], [email protected] Stéphane Mallat CMAP, Ecole Polytechnique [email protected] MS46 Motion Compensation in Computed Tomography

MS46 Clinical applications of computed tomography (CT) often Numerical Analysis of View Dependent Derivatives deal with motion-contaminated data. Examples are carin Computed Tomography diac or respiratory patient motion. We discuss motion- compensated reconstruction with 3D cone beam CT. Cur- A number of CT reconstruction formulas depend on a com- rently there is a well-established theoretical foundation for mon derivative with respect to source position. In fan- exact 3D reconstruction of motionless phantoms, based on beam or helical CT, the derivative can be viewed as the work of Katsevich, Zou, Pan, Noo, Pack, Wang, Chen, and diﬀerence quotient of measurements made along parallel others. However, when motion is introduced, the exactness lines and an accurate numerical implementation is crit- breaks down. When motion is present we need to balance ical to the resolution of the reconstruction. We review exactness with stability to motion. There are known tech- some of the proposed methods to implement the derivative niques to handle motion with approximate reconstruction, and present their corresponding error terms in a common based on work of Kachelriess, Taguchi, Schechter, and oth- framework for fan-beam CT. ers; however these approaches disregard increasing cone angle and not suitable for fully 3D reconstruction. In this Ryan Hass talk we propose an approach that combines elements of ex- Oregon State University act reconstruction with motion-gated reconstruction, and [email protected] show evaluation results.

Alexander Zamyatin MS46 Toshiba Medical Research Analytic and Optimization-based Image Recon- [email protected] struction in Cone-beam CT

CT hardware, algorithms, and applications have experi- MS47 enced tremendous advances in the last two decades. In From Observable Space to Parametric Space (and the presentation, I will focus on discussing recently de- Back): Interpretation of earth formation struc- veloped analytic and optimization-based algorithms for ture from Electro-Magnetic Measurements by image reconstruction in cone-beam CT and their poten- Anisotropic Diﬀusion Maps tial implications for CT applications. Emphasis will be placed on the discussion of diﬀerences between analytic Given empirical data generated by a non-linear transfor- and optimization-based algorithms and their implications mation of some physical parameters we introduce an al- for practical applications. Examples will be used to illus- gorithm that can map newly observed data points back trate and clarify a number of issues, such as the relation- into the invariant parameters space. Moreover, the algo- ship between the Nyquist sampling theorem and compres- rithm can map a new sample from the parameters space IS10 Abstracts 85

to the observable space. The key idea is the use of the MS48 anisotropic diffusion kernel on reference points from the Reconstruction of the Orientation Distribution observed data to approximate a Laplacian on the inacces- Function in Q-Ball Imaging within Constant Solid sible independent parameters space. We demonstrate our Angle method in Logging While Drilling (LWD), to interpret formation structure from Electro-Magnetic Measurements. Q-ball imaging is a high-angular-resolution diffusion imaging technique which has been proven successful in resolving Dan Kushnir multiple intravoxel fiber orientations. The standard com- Department of Mathematics putation of the orientation distribution function (ODF, the Yale University probability of diffusion in a given direction) neglects the [email protected] change in the volume element along each direction. A new technique is proposed here that, by considering the solid angle factor, results in a dimensionless and normalized MS47 ODF expression computed from single or multiple q-shells. Foundations of Multi-Manifold Modeling Algo- rithms Iman Aganj University of Minnesota We present several methods for multi-manifold data mod- Department of Electrical Engineering eling, i.e., modeling data by mixtures of manifolds (possi- [email protected] bly intersecting). We first concentrate on the special but useful case of hybrid linear modeling, where the underly- Christophe Lenglet ing manifolds are affine or linear subspaces. We emphasize Department of Electrical and Computer Engineering various theoretical results supporting the performance of University of Minnesota such algorithms as well as practical choices guided by it. [email protected] This is part of joint works with E. Arias-Castro, G. Chen, A. Szlam, Y. Wang, T. Whitehouse and T. Zhang Guillermo Sapiro Gilad Lerman University of Minnesota Department of Mathematics Dept Electrical & Computer Engineering University of Minnesota [email protected] [email protected] Essa Yacoub, Kamil Ugurbil, Noam Harel Center for Magnetic Resonance Research, U. of Minnesota MS47 [email protected], [email protected], Multiple Scales in High-dimensional Noisy Data [email protected] Sets and Images

We introduce multiscale geometric methods for studying MS48 the geometry of noisy point clouds in high-dimensions, Diffusion Propagator Imaging: Going Beyond Sin- which may model data sets in a variety of applications. gle Shell HARDI These methods allow to estimate in a robust fashion the intrinsic dimensionality of the data, to generate automat- Many recent single-shell high angular resolution diffusion ically dictionaries for the data, and manipulate the data imaging (HARDI) reconstruction techniques have been infor tasks such as denoising and modeling in a way that troduced to reconstruct orientation distribution functions respects the intrinsic geometry of the data. (ODF) that only capture angular information contained in the diffusion process of water molecules. By also consider- Guangliang Chen, Anna Little, Mauro Maggioni ing the radial part of the diffusion signal, the reconstruction Department of Mathematics of the ensemble average diffusion propagator (EAP) of wa- Duke University ter molecules can provide much richer information about [email protected], [email protected], complex tissue microstructure than the ODF. In this talk, I [email protected] will present recent techniques to reconstruct the EAP from multiple shell q-space acquisitions, one of which is named diffusion propagator imaging (DPI). The DPI solution is MS47 analytical and linear because it is based on a 3D spheri- Image De-Noising on the Manifold of Patches: A cal Laplace equation modeling of the diffusion signal. We Spectral Approach validate DPI with simulations, ex vivo phantoms and also illustrate it on an in vivo human brain dataset. This opens Inspired by the work of Lee and Mumford, who showed perspectives in q-space acquisition schemes and lead to new experimentally that 3x3 patches of natural images orga- ways to study white matter anomalies and properties with nize themselves around nonlinear low dimensional mani- the diffusion propagator. folds, we propose to construct basis functions to efficiently parametrize the manifolds of image patches. In this work, Maxime Descoteaux we describe how we can remove the noise from an image by Department of Computer Science iteratively reconstructing and denoising the set of patches. Sherbrooke University This approach outperforms the most successful denoising [email protected] techniques.

Francois G. Meyer Rachid Deriche University of Colorado at Boulder Odyss´ee Lab, INRIA Sophia Antipolis USA [email protected] [email protected] Denis Le Bihan, J.-Fran¸cois Mangin, Cyril Poupon 86 IS10 Abstracts

NeuroSpin, CEA Saclay, France Yunmei Chen [email protected], [email protected], Department of Mathematics [email protected] University of Florida yun@uﬂ.edu

MS48 Xiaojing Ye Recent Advances in Estimation and Processing of Department of Mathematics, University of Florida High Angular Resolution Diffusion Images 358 Little Hall, Gainesville, FL32611-8105 xye@ufl.edu High angular resolution diffusion imaging (HARDI) has become an important magnetic resonance technique for in vivo imaging. The first part of this talk focuses on estimat- Ying Wu ing the diffusion orientation distribution function (ODF) Radiology Department, NorthShore University from raw HARDI signals. We will present an estimation HealthSystem method that naturally constrains the estimated ODF to [email protected] be a proper probability density function and regularizes this estimate using spatial information. By making use of MS49 the spherical harmonic representation, we pose the ODF estimation problem as a convex optimization problem and Blind Motion Deblurring Using Multiple Images propose a coordinate descent method that converges to the We propose a novel method for automatically recovering a minimizer of the proposed cost function. In the second high-quality clear image from multiple blurred images. We part of this talk, we will present a Riemannian framework avoid the bottleneck of previous methods which required to carry out computations on an ODF field. The proposed multiple blurred image frames to be accurately aligned dur- framework does not require that the ODFs be represented ing pre-processing. Here instead, by exploring the sparsity by any fixed parameterization, such as a mixture of von of the motion blur kernel and the clear image under certain Mises-Fisher distributions or a spherical harmonic expan- domains, we propose an alternative approach to simultane- sion. Instead, we use a non-parametric representation of ously identify the blur kernels of given blurred images and the ODF, and exploit the fact that under the square-root restore a clear image. re-parameterization, the space of ODFs forms a Rieman- nian manifold, namely the unit Hilbert sphere. Specifically, Jian-Feng Cai we use Riemannian operations to perform various geomet- CAM - UCLA ric data processing algorithms, such as interpolation, con- [email protected] volution and linear and nonlinear filtering.

Alvina Goh MS49 Department of Biomedical Engineering Flicker Stabilization in Image Sequences Johns Hopkins University [email protected] Flicker is an artefact appearing in old films or in some videos, which is characterized by intensity changes from a frame to another. Some of these contrast changes are not MS48 global and may be localized only on a part of the image. In Regularization of Orientation Distribution Func- this talk, we will introduce a new method to stabilize flicker tions in Diffusion MRI in films. Local contrast changes are performed in order to equalize the grey level distribution of an image patch with Orientation Distribution Functions (ODF) are very impor- the grey level distributions of all its corresponding patches tant in Diffusion Magnetic Resonance Imaging (Diffusion in the previous and following frames. The correspondences MRI). They can be used as probability density functions of a patch are computed thanks to a similarity measure (PDF) when applied to statistical fiber tracking of brain that is built to be robust to contrast changes. tissues. There has been a lot of work on calculation, characterization and regularization of ODFs. To prepare ODFs Agnès Desolneux for fiber tracking, it is best to incorporate global informa- MAP5 - UniversitédeParisDescartes tion in regularization. However, since there are many vox- France els involved in 3D regularization, and for each voxel there [email protected] are several directional data, which makes the global regularization a 4D problem, and it is almost impossible to Julie Delon finish the regularization within a bearable time. There is LTCI - Telecom ParisTech - France no fast algorithms yet published for global 3D regulariza- [email protected] tion of ODFs. We will introduce a new model of global regularization using total variation and wavelet transform. The novelty of our work is that we will implement a fast MS49 and robust method in the calculation of the global model. Fast Dejittering for Digital Video Images Using Lo- With the help of the fast numerical method, it is now viable cal Non-smooth and Non-convex Functionals for us to work on global regularization ODF calculation, which will provide much better ODF results and improve We propose several very fast algorithms to restore jittered the accuracy of brain fiber tractography, in both single fiber digital video frames (their rows are shifted) in one itera- direction cases and multiple fiber direction cases. tion. The restored row shifts minimize non-smooth and possibly non-convex local criteria applied on the second- Yuyuan Ouyang order differences between consecutive rows. We introduce Department of Mathematics, University of Florida specific error measures to assess the quality of dejittering. ouyang@ufl.edu Our algorithms are designed for gray-value, color and noisy frames. They outperform by far the existing algorithms IS10 Abstracts 87

both in quality and speed. jects among many cameras. Once foreground subtraction has been applied and object representations have been de- Mila Nikolova rived we perform semi-supervised clustering given a set of Centre de Mathématiques et de Leurs Applications pairwise constraints provided by the user aided by met- (CMLA) ric learning approaches. Distance metric on the manifold ENS de Cachan, CNRS of Symmetric Positive Definite matrices is represented as [email protected] an L2 distance in a vector space and a Mahalanobis-type distance metric is learnt in the new space in order to improve the performance of semi supervised clustering. We MS49 will present results in clustering people appearances from Restoration of Home Movies single and multiple camera views. Home movies are short films, usually produced by ama- Vassilios Morellas teurs, which have high cultural and historical value. The Department of Computer Science and Engineering home movie archive of the Catholic University of Uruguay University of Minnesota has a large collection of movies, some in traditional film [email protected] support and others in Umatic tapes. We explored the specificities of each material and the best way to restore them while preserving its original content. In the talk we MS50 will present the obtained results. Adaptive Detection of Objects in Hyperdimen- sional Images via Domain-reducing Mappings Alvaro Pardo DIE, Universidad Católica del Uruguay Adaptive object detectors whiten image backgrounds and [email protected] then match-filter. When the number of degrees of freedom is large (e.g., hyperdimensional case), there may be insufficient data for estimating background statistics. We MS50 present optimal and near-optimal mappings for projecting An Approach of Feature Detection and Fusion in hyperdimensional images into reduced domains and detect- Facial Recognition ing objects of interest therein. The inverse problem: back- projecting the adaptive weights into the original domain, is Currently, most facial recognition algorithms work under also discussed, as this is of practical importance to ill-posed controlled environments. In real applications, a trade-off problems (e.g., tomography applications). exists between efficiency and accuracy. We proposed an approach that performs fusion on the face area and fa- Firooz Sadjadi, Manuel F. Fernandez, Tom Aridgides cial components (eyes, nose, and mouth). These compo- Lockheed Martin Corporation nents are also compared to the respective features of other fi[email protected], [email protected], faces. The proposed approach has yielded promising re- [email protected] sults that demonstrate the benefits of fusion technology. High-resolution images are quickly processed to detect and recognize slightly-angled faces accurately. MS51 Global Weak Solutions for Some Nonlinear Diffu- Roland Cheng sions Defence R&D Canada Ottawa [email protected] A family of nonlinear nonlocal diffusions is analyzed which interpolates between a Perona-Malik type equation and regular linear diffusion via the use of fractional derivatives. MS50 Solvability, global existence of strong and of a kind of weak Automated Sea Mine Detection, Classification, and solutions as well as transition from non-trivial nonlinear to Fusion in Sonar Data trivial diffusive behavior will be analyzed and numerically demonstrated. The Office of Naval Research (ONR) has sustained significant research in automated sea-mine detection and clas- Patrick Guidotti sification (D/C). This paper presents an overview of au- University of California at Irvine tomated D/C processing for high-resolution side-looking [email protected] sonar imagery including: normalization of sonar imagery, D/C algorithms, and Algorithm Fusion (combining multiple D/C algorithms). Results from recent exercises MS51 are given. Finally the paper presents current technical Multiphase Scale Segmentation approaches regarding ONR’s new focus on buried-mine D/C, exploiting multi-spectral and multi-aspect data from Variational approaches to image segmentation has been broadband synthetic aperture sonars. widely studied, specially since Mumford-Shah functional was proposed. Various extensions have been studied in- Gerald J. Dobeck cluding multiphase segmentation. This talk will focus on NSWC PC multiphase segmentation using size of the objects in the [email protected] image.

Sung Ha Kang MS50 Georgia Inst. of Technology Metric Learning for Semi-supervised Clustering of Mathematics Object Representations [email protected] Practical image processing systems require matching of ob- 88 IS10 Abstracts

MS51 Jing Yuan On the Construction of Topology-preserving Defor- Department of Computer Science, The University of mation Fields Western On [email protected] In this paper, we investigate a new method to enforce topology preservation on two-dimensional deformation fields. Xue-cheng Tai The method is composed of two steps: - the first one con- Dept. of Mathematics, University of Bergen, Norway and sists in correcting the gradient vector fields of the defor- Div. of Math. Sciences, Nanyang Tech. University mation at the discrete level, in order to fulfill a set of con- [email protected] ditions ensuring topology preservation in the continuous domain after bilinear interpolation. This part, although related to prior works by Karacali and Davatzikos (Es- MS52 timating Topology Preserving and Smooth Displacement Statistical and Computational Methods in Object Fields, B. Karacali and C. Davatzikos, IEEE Transactions Recognition on Medical Imaging, vol. 23(7), 2004), proposes a new approach based on interval analysis. - the second one aims This course will cover existing algorithms and future chal- to reconstruct the deformation, given its full set of discrete lenges for object recognition with a focus on statistical gradient vector fields. The problem is phrased as a func- models and computational issues. We will consider three tional minimization problem on a convex subset K of an main tasks in the area. The first involves classification Hilbert space V. Existence and uniqueness of the solution of images containing a single object. The second involves of the problem are established, and the use of Lagrange’s the detection of objects from a particular class in large multipliers allows to obtain the variational formulation of cluttered images. The third involves the challenge of label- the problem on the Hilbert space V. Experimental results ing multiple interacting objects in an image. We will con- demonstrate the efficiency of the method. Comparisons sider both generative and discriminative models, emphasiz- and comments on the major differences between our model ing their differences and similarities in terms of modeling, and the one introduced by Karacali and Davatzikos are also training and computation. Specific topics will include the provided notion of invariances, low-level features, intermediate representations, learning from weakly labeled data and part- Dominique Apprato based models. Universite de Pau Dept Mathematique Recherche Yali Amit [email protected] University of Chicago Dept. of Statistics Christian Gout [email protected] Universite de Valenciennes, France chris [email protected] Pedro Felzenszwalb University of Chicago Carole Le Guyader pff@cs.uchicago.edu INSA Rouen, France [email protected] MS53 Frame Methodology for Dimension Reduction MS51 Global Minimization for Continuous Multiphase Motivated by hyperspectral imaging problems, we con- Partitioning Problems using a Dual Approach struct a frame-based algorithm for dimension reduction and classification. The algorithm is formulated in terms This talk is devoted to the optimization problem of contin- of kernel methods, frame potential energy, and constraint- uous multi- partitioning, or multi-labeling, which is based based optimal frames. The output of the algorithm is a on a convex relaxation of the continuous Potts model. We data dependent frame. Sparse representation techniques prove that optimal solutions to this re- laxed problem is ensure that this frame provides a frame element for each in fact integer valued and globally optimal to the Pott Rs class to be identified to the exclusion of the other classes. model! In contrast to previous efforts, which are trying The reduced dimension can be less than the number of to tackle the optimal labeling problem in a direct man- classes to be analyzed. ner, we first propose its novel dual model and then build up a corresponding duality-based approach. By this, the John J. Benedetto close connections between optimal labelings and geomet- University of Maryland rical clustering of spatial points are revealed. In order to College Park deal with the highly nonsmooth dual problem, we suggest a [email protected] smoothing method based on the log-sum exponential function and also indicate that such smoothing approach for- MS53 mally gives rise to the novel smoothed primal-dual model and suggests labelings with maximum entropy. As shown Processing and Compressing DTED and Hyper- in the numerical experiments, such smoothed method for spectral Data the dual model produces an expectation maximization We have developed new algorithms for compressing and like algorithm for the multi-labeling problem and yields denoising DTED data, including multiple returns. We also better numerical results. have incorporated a new method for unmixing hyperspec- Egil Bae tral data using a recently developed algorithm of Arthur University of Bergen Szlam. We will discuss these techniques and give applica- [email protected] IS10 Abstracts 89

tionsandideasforfuturework. MS54 Convex Source Support in Half-plane Stanley J. Osher University of California We extend the concept of convex source support to the Department of Mathematics framework of inverse source problems for the Poisson equa- [email protected] tion in an insulated half-plane. The convex source support is, in essence, the smallest convex set that supports a source that produces the measured data. We modify a MS53 previously introduced method for reconstructing the con- Full and Partial Pixel Methods for Spatial/spectral vex source support in bounded domains to our unbounded Pattern Analysis setting. The resulting algorithm is also applied to the electrical impedance tomography. Automated classification methods are typically full-pixel techniques that render hardened class labels at each site Lauri Harhanen in an image. Often the labeling is made too soon in the Aalto University overall decision process and the results are unreliable. In Department of Mathematics and Systems Analysis this study, a sub-pixel method constrained by full-pixel [email protected].fi processes is applied to hyperspectral imagery resulting in ”soft” class map layers for subsequent object recognition Nuutti Hyvönen and terrain analysis. The context is terrain, urban, and Institute of Mathematics shallow-water mapping. Helsinki University of Technol Robert Rand [email protected].fi National Geospatial-Intelligence Agency [email protected] MS54 Backscattering in Electrical Impedance Tomogra- MS53 phy High-Dimensional Methods Applied to Summariz- Electrical impedance tomography is an imaging technique ing, Indexing, and Search Full-Motion-Video for recovering the admittance inside a body from boundary The pace at which full motion video is being collected, from measurements of current and voltage. If the measurement persistent and mobile surveillance systems, is accelerating probe is small, consists of two electrodes and can be moved at such a fast pace that arent enough human eyeballs to along the boundary, the resulting data is of backscatter- monitor or analyze the volume of data. By taking advan- ing nature. We note that such measurements uniquely tage of a convergence of new analytics methods and ad- determine an insulating inclusion in constant background. vanced multi/many-core computing architectures this vol- Moreover, we present an algorithm for reconstructing the ume of video data can be reduced to a manageable set of so-called convex backscattering support of a more general high-compressed, content-based summarization and index inhomogeneity. tables that can facilitate the searching and analysis of the Nuutti Hyvönen data for objects and events. This presentation describes Helsinki University of Technology the use of sparse representations to build a content based Institute of Mathematics search engine for searching full motion EO and IR, and nuutti.hyvonen@hut.fi video data. Harold E. Trease Martin Hanke Pacific Northwest National Laboratory Joh. Gutenberg-Universität [email protected] Mainz, Germany [email protected]

MS54 Stefanie Reusswig Reconstruction of Thin Tubular Objects from Elec- Johannes Gutenberg-Universit¨at Mainz tromagnetic Scattering Data [email protected]

We consider the inverse problem of reconstructing a collection of thin tubular objects from measurements of electro- MS54 magnetic scattering data. In potential applications these Detecting Anomalies in Electrical Impedance To- objects could, e.g., be wires or tubes buried in the sub- mography surface. Applying an asymptotic representation formula for the scattered ﬁeld as the thickness of the scatterers The factorization method for electrical impedance tomog- tends to zero, we establish an asymptotic characterization raphy (EIT) is a successful method for the detection of of these scatterers in terms of the measurement data. This anomalies, i.e. domains in which the conductivity is dif- characterization is then implemented in a non-iterative re- ferent from the background conductivity. However, it is construction algorithm. a qualitative method, i.e. it doesn’t provide the conductivity inside the anomalies. We present a new version of Roland Griesmaier the factorization method for EIT and show that it leads to University of Delaware a method to compute this conductivity inside previously Department of Mathematical Sciences located anomalies. [email protected] Susanne Schmitt Universit¨at Karlsruhe Institute for Algebra and Geometry 90 IS10 Abstracts

[email protected] super-resolution. In the formulation of nonlocal variational models for the image deblurring with impulse noise, we propose an eﬃcient preprocessing step for the computation of MS55 the weight function. In all the applications, the proposed Variational Restoration of Images with Space- nonlocal regularizers produce superior results over the local Variant Blur ones.

We address the problem of space-variant image deblur- Miyoun Jung ring, where different parts of the image are blurred by Department of Mathematics different blur kernels. Assuming a region-wise space vari- UCLA ant point spread function, we first solve the problem for [email protected] the case of known blur kernels and known boundaries between the different blur regions in the image. We then Xavier Bresson generalize the method to the challenging case of unknown UCLA boundaries between the blur domains. Using variational Department of Mathematics and level set techniques, the image is processed globally. [email protected] The space-variant deconvolution process is stabilized by a unified common regularizer, thus preserving discontinuities Tony Chan between the differently restored image regions. We address University of California. Los Angeles the cases of space-variant out-of-focus blur, and simultane- [email protected] ous motion estimation, blur segmentation and restoration. Luminita A. Vese Leah Bar University of California, Los Angeles University of Minnesota Department of Mathematics [email protected] [email protected]

MS55 MS55 Mathematical and Computational Techniques for Computational Approaches for Multi-Frame Blind Inverse Problems with Poisson Data Deconvolution In image processing, Poisson data arises when intensities Multi-frame deconvolution (MFBD) requires using itera- are measured via counting processes, e.g., when a CCD tive methods to solve large scale, nonlinear optimization camera is used and in positron emission tomography. The problems. In this talk we describe an efficient variable pro- resulting Poisson maximum likelihood reconstruction prob- jection Gauss-Newton method to solve the MFBD problem presents both computational and mathematical chal- lem. Tikhonov regularization is incorporated using an it- lenges. For one, regularization is typically needed, which erative Lanczos hybrid scheme, where regularization pa- leads to theoretical questions in the realm of classical reg- rameters are chosen automatically using a weighted gener- ularization theory and to the problems of regularization alized cross validation method, thus providing a nonlinear parameter and operator choice. Also, the resulting compu- solver that requires very little input from the user. In ad- tational problem, being large-scale and nonnegatively condition, we consider approaches that incorporate nonnega- strained, is challenging and requires an efficient method. In tivity constraints and preconditioning, which provide both this talk, we will present some results that we’ve obtained additional prior information and help to improve compu- in our effort to address these disparate challenges. tational efficiency. Johnathan M. Bardsley James G. Nagy University of Montana Emory University [email protected] Department of Math and Computer Science [email protected]

MS55 Image Restoration Using Nonlocal Mumford-Shah MS55 Regularizers Space-Continuous Models and Algorithms for Im- age Deconvolution We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image in- To introduce to the thematic spectrum of the min- formation. The standard Ambrosio-Tortorelli and Shah isymposium, the talk will start with an overview over models are defined to work in a small local neighborhood, minimisation-based approaches to image deconvolution. which are sufficient to denoise smooth regions with sharp Afterwards it will focus on variational models and present boundaries. However, textures are not local in nature and methods to accommodate the positivity constraint within require semi-local/non-local information to be denoised ef- such models. Firstly, this includes a reparametrisation ap- ficiently. Inspired from recent works such as NL-means of proach in connection with a gradient descent technique. Buades, Coll, Morel and NL-TV of Gilboa, Osher, we ex- Reinterpretations then lead to differential-geometric mod- tend the standard models of Ambrosio-Tortorelli and Shah els on one hand, and to interesting new fixed-point itera- approximations to Mumford-Shah functionals to work with tions on the other hand. nonlocal information, for better restoration of fine structures and textures. We present several applications of Martin Welk the proposed nonlocal MS regularizers in image processing Mathematical Image Analysis Group such as color image denoising, color image deblurring in Saarland University the presence of Gaussian or impulse noise, and color image [email protected] IS10 Abstracts 91

MS56 speaking, the problem is to automatically find correspon- Discrete Optimization via Graph Cuts for Nonrigid dences between points in two different images. This talk Registration provides a brief introduction to image registration and out- lines a general framework, which is based on a variational In this presentation, we formulate non-rigid image regis- approach. The talk also introduces the freely available soft- tration as a discrete labeling problem. Each pixel in the ware FAIR (Flexible Algorithms for Image Registration). source image is assigned a displacement label (which is a Based on a variety of examples, it is demonstrated, why vector) indicating which position in the floating image it is the software is useful and how it can be used. spatially corresponding to. A smoothness constraint based on the first derivative is used to penalize sharp changes in Jan Modersitzki displacement labels across pixels. The whole system can McMaster University be optimized by using the graph-cuts method via alpha- Department of Computing and Software expansions. We compare 2D and 3D registration results of [email protected] our method with two state-of-the-art approaches. Albert Chung MS57 Dept. of Comp. Sci. and Eng. Sampling Over Infinite Unions: Towards Compres- Hong Kong Univ. of Sci. & Tech. sive Ultrasonic Imaging [email protected] Real-time cardiac ultrasound suffers from complexity due to high sampling rates. Our goal is to reduce this rate by MS56 exploiting the mathematical structure of ultrasound im- Optimization Based Methods for Non-Rigid Image ages, captured by a union of subspaces model. We develop Registration extensions of compressed sensing (CS) to the general union model including continuous-time signals by combining CS In my talk I will focus on numerical methods for non- ideas with traditional analog sampling theory, leading to rigid registration based on optimization. Starting from a a framework we coin Xampling (CS+sampling). We then variational formulation we discretize the registration prob- apply Xampling to reduce the complexity of ultrasound lem and apply efficient Newton-type optimization meth- imaging. ods such as Gauss-Newton or limited memory BFGS. Fur- thermore, I will demonstrate how to incorporate addi- Yonina C. Eldar tional knowledge and requirements from applications such Technion and Stanford as landmarks or control of local volume changes by con- [email protected] straint optimization. Stefan S. Heldmann MS57 University of Lübeck Sampling, Reconstruction, and Recognition of Vi- Institute of Mathematics sual Signals Guided by Self-similarity [email protected] We present a non-parametric framework based on the notion of Kernel Regression which we generalize to adapt to MS56 local geometric characteristics of the given signal. These Variational Registration with Free Form Deforma- descriptors are exceedingly robust in capturing the under- tions lying structure of multidimensional signals even in the presence of significant noise, missing data, and other distur- Traditionally dense deformable registration and grid based bances. This framework is applicable to a wide variety of (such as free form using b-splines) deformable registration problems. Of particular interest in two and three dimen- are numerically solved using different approaches. Dense sions are sampling and restoration. Of recent relevance to deformable registration problem is usually formulated as an computer vision, are applications to object and action de- iterative partial differential equation and efficiently solved tection/recognition in images, and in video, respectively, using semi-implicit approaches. On the other hand, for from a single example. free from deformable (FFD) registration problem explicit gradient-based approaches are used. In this talk, we out- Hiroyuki Takeda line a unified approach for solving these problems. We UC Santa Cruz show that the grid based approaches can be interpreted [email protected] as a dense deformable registration, where the interpolation kernel is built in the regularization constraint. Using this Hae Jong Seo, Peyman Milanfar unified approach, we gain computational efficiency while EE Department not compromising the quality of the match and the defor- University of California, Santa Cruz mation field. The empirical results show the promise of the [email protected], [email protected] proposed approach.

Ali Khamene MS57 Siemens Corporate Research Optical Image Reconstruction from Binary Sensors [email protected] We propose an optical setup for the acquisition of image data using binary sensors, which is a special form of com- MS56 pressed sensing. We address the ill-posedness of the prob- FAIR: A Toolbox for Image Registration lem by imposing a penalty on the total variation of the solution. We derive the image reconstruction algorithm Image registration is one of the challenging tasks in image based on the minimization of a corresponding convex func- processing and in particular in medical imaging. Roughly 92 IS10 Abstracts

tional. We illustrate the feasibility of the approach with denoising 3D MRI datasets. Our tests sweep comparable some concrete examples. parameters for the two filters and measure total runtime, memory bandwidth, computational throughput, and mean Michael A. Unser,Aurélien Bourquard squared errors relative to a noiseless reference dataset. To EPFL assess the suitability of these implementations and param- michael.unser@epfl.ch, aurelien.bourquard@epfl.ch eter choices for an image processing pipeline, we also perform segmentation and calculate validation scores.

MS57 Mark Howison ‘Rewiring’ Filterbanks for Interpolation and De- Lawrence Berkeley National Laboratory noising: Theory and Applications [email protected] This article describes a series of new results outlining equiv- alences between certain “rewirings’ of filterbank system MS58 block diagrams, and the corresponding actions of convolu- Combining Imagery, Documents, Audio, and Video tion, modulation, and downsampling operators. This gives in a Multi-Domain Data Space rise to a general framework of reverse-order and convolution subband structures in filterbank transforms, which Technology has allowed for data collection from multi- we show to be well suited to the analysis of filterbank co- ple domains, however the methods by which this data is efficients arising from subsampled or multiplexed signals. scoured has not advanced in the same way. Data searches These results thus provide a means to understand time- still rely on single-domain searches. This precludes the use localized aliasing and modulation properties of such signals of inter-domain linkages that are inherent in natural data. and their subband representations—notions that are no- In this work, a set of multiple-domain subspaces are cre- tably absent from the global viewpoint afforded by Fourier ated such that a query of one type of data can directly analysis. The utility of filterbank rewirings is demon- recall data from all other domains strated by the closed-form analysis of signals subject to degradations such as missing data, spatially or temporally Jason Kinser multiplexed data acquisition, or signal-dependent noise, George Mason University such as are often encountered in practical signal processing Bioinformatics and Computational Biology applications. [email protected]¿ Patrick J. Wolfe Statistics and Information Sciences Laboratory MS58 Harvard University Retinopathy Diagnosis from Ocular Fundus Image [email protected] Analysis

Keigo Hirakawa Eye care can benefit from the use of ocular fundus images to Harvard University diagnose pathologies. The analysis of these images requires University of Dayton automatic identification of normal and aberrant structures [email protected] in human retina such as macula, vascular network, optic disc, hemorrhages, drusen, fovea, exudates, and microa- neurysms. Our algorithms use Hough transform to locate MS58 the optic disk, which facilitates classification of microa- Differential Geometry of Curves for Large-Scale neurysms. We also consider vascular network extraction Multi-View Stereo and Applications to Biomedical and other structures by means of mathematical morphol- Imaging ogy.

We will present a large-scale system for automatic 3D Daniela M. Ushizima reconstruction of arbitrary curves and occluding surfaces Visualization and Math Groups from multiple views. The system is multi-threaded and Lawrence Berkeley National Laboratory scales up to thousands of images at high-definition, and [email protected] handles complex scenes beyond the capabilities of other methods. The use of differential geometry for multiview Fatima Medeiros matching and calibration are shown to be key for achiev- Teleinformatics Engineering Department ing robustness. Biomedical applications which may require Federal University of Ceara, Brazil fast, flexible, low-cost, and non-invasive photogrammetric [email protected] solutions will be discussed. Ricardo Fabbri MS59 Brown University The Unreasonable Effectiveness of Bregman Itera- Computer Engineering tion for L1 Type Opimization [email protected] Bregman iteration was introduced to TV based restoration a few years ago and improved the performance signif- MS58 icantly. Later it was found that this same idea gave what Comparing GPU Implementations of Bilateral and appear to be state-of-the-art fast algorithms for L1 based Anisotropic Diffusion Filters for 3D Biomedical optimization problems arising in compressive sensing and Datasets elsewhere. Not only has this method been around since 1967, but every new variant recently invented appears to We compare the performance of hand-tuned CUDA imple- be closely related to and indeed often a special case of mentations of bilateral and anisotropic diffusion filters for known techniques. So why is it a so important now? The IS10 Abstracts 93

answer seems to be found in the nature of L1 itself. Errors plication to Single-Pixel Camera cancel beautifully. I will discuss this here. This is joint work with Wotao Yin and many other collaborators. We propose and study the use of the classic Augmented Lagrangian Method in image reconstruction in compres- Stanley J. Osher sive sensing. The subproblems involved are solved through University of California a variable splitting and alternating minimization scheme. Department of Mathematics The resulting Matlab code, called TVAL3, is compared [email protected] with several state-of-the-art codes on both synthetic data and real data measure by the Rice single-pixel camera. MS59 Yin Zhang, Chengbo Li FPC AS: A Fast Algorithm for Sparse Reconstruc- Rice University tion Based on Shrinkage and Subspace Optimiza- Dept of Comp and Applied Math tion [email protected], [email protected]

We describe a fast algorithm for sparse reconstruction. The Wotao Yin algorithm is divided into two stages that are performed re- Rice University peatedly. In the first stage, “shrinkage” yields an estimate [email protected] of the subset of variables likely to be nonzero in an optimal solution. Subspace optimization are then used to recover the magnitude of the solution in the second phase. MS60 Our implementation of this method exhibits state-of-the- Challenges in Developing a DWI/DTI Pipeline art performance both in terms of its speed and its ability to recover sparse signals. While diffusion MRI is already an established field, its potential clinical applications are still in a formative stage. Zaiwen Wen One impediment to the implementation of diffusion MRI Columbia University is the dearth of an established analysis framework to enable [email protected] one to make valid statistical inferences and draw meaningful scientific conclusions, particularly from longitudinal and Wotao Yin multi-center data. Some unresolved issues will be described Rice University whose resolution would help ensure that these studies will [email protected] produce high-quality findings.

Donald Goldfarb Peter J. Basser Columbia University National Institutes of Health [email protected] [email protected]

Yin Zhang MS60 Rice University Optimal Sampling Schemes for Diffusion MRI Ac- Dept of Comp and Applied Math quisitions and Online Models Estimation [email protected] High angular resolution diffusion magnetic resonance imaging has been widely used in research. However, its clinical MS59 use remains hindered by its demand in acquisition time. A Review and Recent Results of the Bregman New trends propose to reconstruct the diffusion model in Methods real-time, thus providing more flexible protocols, which can be switched off or continued on demand. These techniques We review four Bregman methods that arise in applica- raise new challenges, we present recent advances in mod- tions of imaging, compressed sensing, and other inverse els estimation and acquisition design with respect to these problems. We explain their numerical properties and high- considerations. light their relationships with the augmented Lagrangian and alternating direction methods. Recent results on the Emmanuel Caruyer Odyssée Project Team INRIA Sophia Antipolis-Méditerranée Bregman methods are included. Applied to the 1-type [email protected] regularization, the original Bregman method has an exact error cancellation property that leads to machine-precision Iman Aganj solutions. In addition, we briefly show an exact penalty University of Minnesota property of the linearized Bregman method. These prop- Department of Electrical Engineering erties explain the great preformance of the Bregman meth- [email protected] ods. The analysis and discussions broadly apply to polyhe- dral regularization functions such the (weighted) 1-norm, Christophe Lenglet anisotropic total variation, piece-wise linear functions. Department of Electrical and Computer Engineering Wotao Yin University of Minnesota Rice University [email protected] [email protected] Guillermo Sapiro University of Minnesota MS59 Dept Electrical & Computer Engineering An Efficient Tv-Minimization Algorithm with Ap- [email protected] 94 IS10 Abstracts

Rachid Deriche cases and modifications. In particular, we point out a con- Odyssée Lab, INRIA Sophia Antipolis vergence result for a modified version of PDHG that has [email protected] a similarly good empirical convergence rate for total variation (TV) minimization problems. Its convergence follows from interpreting it as an inexact Uzawa method discussed. MS60 We also prove a convergence result for PDHG applied to A Finite Element Based Method for Quantification TV denoising with some restrictions on the PDHG step size of Self-diffusion Process in White Matter Environ- parameters. It is shown how to interpret this special case ment as a projected averaged gradient method applied to the dual functional. We discuss the range of parameters for Diffusion MRI (DMRI) is a biomedical imaging modality which the inexact Uzawa method and the projected aver- for non-invasive assessment of anatomy of white matter aged gradient method can be shown to converge. We also tracts in human brains. It offers local sensitivity of white present some numerical comparisons of these algorithms matter tracts to orientations of water molecules diffusive applied to TV denoising, TV deblurring and constrained motions. To simulate the DMRI process, we develop a l1 minimization problems. higher-order finite element method for solving the diffusion PDE in a multi-compartment environment in this work, Ernie Esser which provides more flexibility for geometry and material UCLA Mathematics Department of different white tracts compartments than existing tech- University of California Los Angeles niques. [email protected]

Shahryar Karimi-Ashtiani Xiaoqun Zhang University of Southern California, Los Angeles, CA University of California Los Angeles. [email protected] [email protected]

C. C. Jay Kuo Tony Chan University of Southern Caliﬁornia, Los Angeles, CA University of California. Los Angeles [email protected] [email protected]

MS60 MS61 Shore in Action: Estimation of Microstructural Dynamic Network Flows and Nonlinear Discrete Features from Magnetic Resonance (MR) Data Total Variation Evolutions Analysis of diffusion-weighted MR data characterizes the We consider combinatorial minimization algorithms for microstructural features of materials or tissues. The Simple solving some variational image processing problems. In Harmonic Oscillator based Reconstruction and Estimation particular, we consider energies involving Discrete Total (SHORE) technique, which successfully represents a wide Variations. Their minimizations yield a differential inclu- range of MR signal profiles, will be described. We will dis- sion problem that can be efficiently solved via parametric cuss how the SHORE framework can be utilized to quantify maximum-flow. A maximum-principle follows. Links with several characteristics of the specimen including its struc- first-order methods, Hamilton-Jacobi equations and con- tural anisotropy, pore size distributions, and an apparent servations are described. fractal dimension. Jerome Darbon Evren Ozarslan, Cheng Guan Koay UCLA Section on Tissue Biophysics and Biomimetics, NICHD [email protected] National Institutes of Health [email protected], [email protected] MS61 Timothy M. Shepherd Non-local Regularization of Inverse Problems Department of Radiology & Biomedical Imaging University of California, San Francisco This article proposes a new framework to regularize lin- [email protected] ear inverse problems using a total variation prior on an adapted non-local graph. The non-local graph is optimized NOAM Shemesh, YORAM Cohen to match the structures of the image to recover. This allows School of Chemistry a better reconstruction of geometric edges and textures Tel Aviv University, Israel present in natural images. A fast algorithm computes iter- [email protected], [email protected] atively both the solution of the regularization process and the non-local graph adapted to this solution. The graph Peter J. Basser adaptation is particularly efficient to solve inverse problems National Institutes of Health with randomized measurements such as inpainting random [email protected] pixels or compressive sensing recovery. Our non-local regularization gives state of the art results for this class of inverse problems. On more challenging problems such as MS61 image super-resolution, our method gives results compara- A General Framework for a Class of First Order ble to translation invariant wavelet-based methods. Primal-Dual Algorithms for TV Minimization Gabriel Peyré We generalize the primal-dual hybrid gradient (PDHG) al- Ceremade, Université Paris Dauphine gorithm proposed by Zhu and Chan, draw connections to [email protected] similar methods and discuss convergence of several special IS10 Abstracts 95

Sebastien Bougleux establishing two diﬀerent hierarchies of lower bounds, we University of Caen relate our distance to previously proposed spectral invari- GREYC CNRS ants used for shape comparison, such as the spectrum of [email protected] the Laplace-Beltrami operator and statistics of pair-wise diﬀusion distances. Lower bounds in these hierarchies pro- Laurent D. Cohen vide increasing discriminative power at the expense of more CNRS, UMR 7534 involved computations. Universite Paris-Dauphine, CEREMADE [email protected] Facundo Memoli Stanford University, Mathematics Department [email protected] MS61 Image Restoration by Tikhonov Regularization MS62 Based on Generalized Krylov Subspace Methods On the Localization Behavior of Graph Laplacian We describe Tikhonov regularization of large linear dis- Eigenfunctions Over Dendrite Structures crete ill-posed problems with a regularization operator of general form and present an iterative scheme based on a We report our observation and analysis of the eigenvalue generalized Krylov subspace method. This method simul- distribution of the Laplacian of graphs representing neu- taneously reduces both the matrix of the linear discrete ronal dendrite patterns, and the behavior of the corre- ill-posed problem and the regularization operator. The responding eigenfunctions. In particular, we discuss a “phase duced problem so obtained may be solved, e.g., with the transition’ phenomenon occurring at the eigenvalue 4. The aid of the singular value decomposition. Also, multipa- eigenfunctions corresponding to the eigenvalues below 4 are rameter Tikhonov regularization is discussed. Numerical semi-global oscillations (like Fourier modes) over the den- results illustrate the promise of problem-oriented operator drite arbors whereas those corresponding to the eigenvalues in image denoising and deblurring. above 4 are localized (like wavelets) in branching regions. Fiorella Sgallari Naoki Saito,ErnestWoei University of Bologna Department of Mathematics Department of Mathematics-CIRAM University of California, Davis [email protected] [email protected], [email protected]

Reichel Lothar MS62 Department of Mathematical Sciences, Kent State The Multiscale Flat Norm for Shape Signatures University [email protected] In this talk, I will discuss the application of the New Mul- tiscale Flat Norm to shapes. Computations are carried Qiang Ye out using graph cut methods with 16 neighbors. As a re- Dept of Math sult the minimizers computed are actually minimizers of Univ of Kentucky an anisotropic energy that approximates the usual TV en- [email protected] ergy. Some details, involving a simple but cumbersome least squares calculation, yields slightly better weights than those which are obtained through the usual Crofton’s For- MS62 mula method. Multiscale Geometry and Probability Measures on Plane Curves Kevin R. Vixie,KeithClawson Washington State University We will construct some families of probability measures on [email protected], [email protected] equivalence classes of plane curves, where the equivalence relations depend on the local regularity of the curve at Brandon Price diﬀerent scales. We will also discuss sampling from these Walla Walla University distributions. [email protected] Matt Feiszli Yale, Mathematics Gary Sandine [email protected] Los Alamos National Laboratory [email protected]

MS62 Thomas J. Asaki Spectral Gromov-Wasserstein Distances for Shape Washington State University Matching and the Role of Scale [email protected]

We introduce a spectral notion of distance between shapes (closed Riemannian manifolds) and study its theoretical MS63 properties. We show that our distance satisﬁes the prop- Numerical Methods for Optimal Mass Transport erties of a metric on the collection of isometry classes with Applications to Image Registration of Riemannian manifolds. Our construction is similar to the Gromov-Wasserstein distance, but rather than view- Optimal mass transport refers to an optimization problem ing shapes as metric spaces, we deﬁne our distance via in which mass is optimally transported. In recent work, the comparison of heat kernels. This is possible since the Benmou and Brenier have shown that although the orig- heat kernel characterizes the shape up to isometry. By inal formulation is highly nonlinear and non-convex it is 96 IS10 Abstracts

possible to reformulate the problem as a convex, PDE con- as an efficient procedure for non-linear registration, the al- strained optimization problem. In this talk we consider gorithm was revisited several times to be recast in a sound efficient numerical techniques for the solution of the re- minimization framework, in particular through Cachier’s sulting problem. We show that the formulation leads to pair and smooth (PASHA) method. Additional modifica- a problem a-kin to nonlinear flow in porous media. We tions were performed bu Stefanescu to make it fully par- then discuss discretization and effective multigrid solution allelizable and to include a non-stationnary adaptive reg- to the problem ularization that could take into account pathologies (areas that do no correspond). Recently, Vercauteren adapted Eldad Haber the efficient optimization procedure to work on a space of Department of Mathematics diffeomorphic transformations, which leads to the diffeo- The University of British Columbia morphic demons. Our experiments show that the results [email protected] are similar in terms of image similarity metric, but more regular and closer to the true transformation in controlled Raya Horesh experiments, particularly in terms of Jacobian. Follow- Emory University ing the proposition of Arsigny to parameterize (some of) Atlanta, GA the diffeomorphism using one parameter subgroups, we will [email protected] finally present the symmetric version and the statistical framework on diffeomorphisms that we could build on it results. MS63 Gauss-Newton Optimization in the Large Deforma- Xavier Pennec tion Diffeomorphic Metric Mapping INRIA Sophia-Antipoolis Meditrerranee [email protected] The Large Deformation Diffeomorphic Metric Mapping (LDDMM) can be considered among the pioneering paradigms for diffeomorphic registration in Computational MS63 Anatomy. Although LDDMM is embedded into a rigorous Unbiased Nonlinear Image Registration mathematical framework where anatomical variability can be properly studied, the huge computational complexity We present a novel unbiased nonlinear image registration inherent to the use of the non-stationary parameterization technique. The unbiased framework generates theoretically of diffeomorphisms constitutes its important practical lim- and intuitively correct deformation maps, and is compati- itation. In order to alleviate the computational require- ble with large-deformation models. We apply information ments of LDDMM, different variations focused on diffeo- theory to quantify the magnitude of deformations and ex- morphism characterization have been proposed in the liter- amine the statistical distributions of Jacobian maps in the ature. Much less attention has been paid to the optimiza- logarithmic space. tion strategy in LDDMM, where classical gradient descent is often used. As shown in alternative non-rigid registra- Igor Yanovsky tion paradigms, the use of efficient second-order optimiza- Jet Propulsion Laboratory, California Institute of tion techniques may improve the rate of convergence during Technolog optimization thus reducing time requirements in LDDMM [email protected] with an affordable increase of the needed memory per iteration. In this talk, I will present a numerical implementation Alex Leow of Gauss-Newton’s method for second-order optimization University of Illinois, Chicago in LDDMM for both non-stationary and stationary param- [email protected] eterizations. The computations of the Gateaux derivatives of the corresponding objective functions are performed in Stanley J. Osher the tangent bundle of the Riemannian manifold of diffeo- University of California morphisms. Two different approaches for the computa- Department of Mathematics tion of the Gateaux derivatives associated to the station- [email protected] ary parameterization of diffeomorphisms lead to two different algorithms for Gauss-Newton stationary LDDMM. Paul M. Thompson The three proposed Gauss-Newton LDDMM methods have Department of Neurology been compared to their respective versions of gradient de- UCLA School of Medicine scent LDDMM using the non-rigid registration evaluation [email protected] project (NIREP) databases. I will report the advantages of Gauss-Newton with respect to gradient descent optimization for the three methods. Finally, I will also show the MS64 advantages of performing optimization in the tangent bun- SD-OCT Image Segmentation in Retinal Pathology dle with respect to optimization in the space of squared Assessed with Adaptive Optics integrable functions proposed in Dartel. Our lab uses adaptive optics ophthalmoscopy to image the Monica Hernandez cone mosaic in a variety of retinal pathology. Adaptive op- University of Zaragoza, Spain tics enables visualization of individual cone photoreceptors, [email protected] so we can quantify the degree of degeneration. SD-OCT is a more prevalent imaging technology, and here we present data on extracting information from SD-OCT images in MS63 these clinical cases. Common metrics like layer thickness Diffeomorphic Demons for Image Registration can be insensitive to dramatic cone disruption, so alternative image analysis tools are needed. In this talk, we will present the evolution of the demons’ algorithm over a decade. Originally proposed by Thirion Joseph Carroll IS10 Abstracts 97

Medical College of Wisconsin quisition and visualization methods as well as data pro- [email protected] cessing techniques has to be implemented. We will describe our AO-UHR-OCT system and techniques developed in our Hitesh Tanna laboratory that allow its use for in-vivo clinical imaging. Marquette University @marquette.edu Robert J. Zawadzki University of California Davis [email protected] Diane M. Tait, Jungtae Rha, Pooja Godara, Kimberly E. Stepien Medical College of Wisconsin Steven M. Jones @mcw.edu, @mcw.edu, @mcw.edu, [email protected] Lawrence Livermore National Laboratory @llnl.gov

MS64 Suman Pilli Introduction to SDOCT imaging and Registeration University of California Davis Using Generalized Pseudo-Polar Fourier Grids [email protected]

Fast and accurate estimation of the Fourier transform in Scot S. Olivier polar coordinates has long been a major challenge for many Lawrence Livermore National Laboratory image processing applications. To address this problem, it [email protected] has been proposed to calculate the Fourier transform coefficients on the pseudo-polar coordinates. To acquire bet- John S. Werner ter image registration accuracy, we introduce the general- University of California Davis ized pseudo-polar motion estimation framework that en- [email protected] compasses the classic pseudo-polar and related techniques. Experimental results on neonatal SDOCT images attest to the effectiveness of this method. MS65 Sina Farsiu,NigelChou,CynthiaA.Toth,JosephA.Izatt The Role of Similarity Measures in Face Recogni- Duke University tion [email protected], [email protected], A fundamental challenge in face recognition lies in deter- [email protected], [email protected] mining which steps are important in the recognition of faces. Several studies have indicated the significance of MS64 certain steps in this regard, particularly preprocessing and feature extraction. Surprisingly, however, it has not been Imaging Processing Techniques for Adaptive Op- made clear whether the similarity measures play an im- tics Fourier Domain Optical Coherence Tomogra- portant role in the recognition of faces. Here, we report phy experimental results which suggest that for face recogni- Adaptive optics Fourier domain optical coherence tomog- tion the similarity measures are influential. raphy (AO-FDOCT) is a relatively new retinal imaging Arjun V. Mane technique that provides micron-level axial and lateral reso- Dr. B A Marathwada University, Aurangabad (MS) India lution in the live eye by dynamic correction of ocular aber- [email protected] rations. AO-FDOCT systems contain at least two imagers and require several parallel stages of real-time processing and control for efficient feature extraction, visualization, Ramesh Manza, Karbhari Kale and manipulation. Post-processing algorithms, for exam- Dr. B A M University, Aurangabad ple those for segmentation, registration, and Doppler phase ramesh [email protected], [email protected] retrieval, are used to enhance and discriminate signal from noise or to delineate tissue margins. Both established and MS65 new techniques will be discussed. Person Detection and Tracking for Large-scale Daniel X. Hammer, Mircea Mujat, Nicusor V. Iftimia, Surveillance NuyomLue,R.DanielFerguson Physical Sciences Inc. Person detection and tracking for large sites is challenging [email protected], mu- due to a variety of reasons. The scenes can get crowded, [email protected], [email protected], [email protected], and in such instances crowd segmentation techniques are [email protected] needed to separate individuals. The large areas to be covered may require several non-overlapping cameras, and tracking between them requires person re-identification. MS64 For city-wide surveillance, cameras mounted on mobile Applications of Adaptive Optics - Ultra-high Reso- platforms may be required. This talk is concerned with lution Optical Coherence Tomography for In Vivo research that has been done in the areas of multi-camera Retinal Imaging and Visualization person detection and tracking, crowd segmentation, person reidentification, and person detection for moving cameras. Recent developments in adaptive optics - optical coherence tomography (AO-OCT) allow for real time ultra-high isotropic resolution imaging of the in-vivo retina, offering Thomas B. Sebastian unprecedented insight into its volumetric microscopic and GE Global Research cellular structures. To achieve full potential of this tech- [email protected] nique for clinical ophthalmic applications novel image ac- 98 IS10 Abstracts

MS65 proposed model. Understanding Crowded Visual Scenes Jung-Ha An Most video surveillance/monitoring approaches assume the Mathematics Department capability to reliably track individuals, thus failing in California State University, Stanislaus crowded environments where such tracking is difficult. We [email protected] first model dense crowd scenes using Lagrangian particle dynamics to segment crowd flows and detect flow instabil- Yunmei Chen ities. Then, observing that pedestrian behavior in crowds University of Florida results from collective behavioral patterns evolving from [email protected]fl.edu large numbers of individuals interacting among themselves and the scene geometry, we generate an algorithm for tracking an individual within the crowd. PP0 Image Diffusion and Sharpening Via High-Order Mubarak Shah Sobolev Gradient Flows University of Central Florida [email protected] We utilize Sobolev gradients for image diffusion and sharpening and show that reformulating the gradient flow for the heat equation energy functional under various Sobolev MS65 metrics yields well posed flows both forward and backward. Dimensionality Reduction and Sparsity for Object This opens the door to applications such as image sharp- Recognition ening via reverse diffusion. We present several theoretical results in this direction as well as favourable comparisons A large body of work has been performed recently explor- to the Shock Filter with striking further improvements as ing ideas in dimensionality reduction, sparse representa- the Sobolev order is increased. tions and compressed sensing. Some work has begun to merge machine learning and dimensionality reduction and Jeff Calder, Abdol-Reza Mansouri sparsity, utilizing these ideas to improve image recognition Department of Mathematics and Statistics performance. This talk will focus on usage and perfor- Queen’s University mance of geometric diffusion and sparse representations for [email protected], [email protected] pattern recognition in challenging imaging conditions. Anthony Yezzi Alan Van Nevel School of Electrical and Computer Engineering Image and Signal Processing Branch, Research Georgia Institute of Technology Department [email protected] NAWC, Weapons Division [email protected] PP0 PP0 Improving Small Angle X-Ray Scattering for Mod- ern Computing Use of Machine Vision for Online Estimation of Coal Fines on Conveyor Belts Small angle X-ray scattering (SAXS) is a technique to find the structure of biological macromolecules. Imaging Excessive fines in coal fed to power stations, metallurgi- macromolecules via SAXS is an inverse problem. The dif- cal furnaces and other fixed or fluidized bed reactors can ficulty is that the inverse problem associated with SAXS is cause major problems by adversely affecting the flow of gas ill-posed and ill-conditioned. Traditionally, many physical through the solid burden. In this industrial case study, the simplifications are made to work around this. The CSU novel application of machine vision to monitor coal on con- SAXS group is proposing to strengthen SAXS with a new veyor feed systems is described. By making use of a mod- modeling approach and new computationl methods that do ified adaptive thresholding algorithm, the fines content in not impose these simplifications. the stratified coal could be estimated reliably. Ryan Croke Chris Aldrich Colorado State University Department of Process Engineering [email protected] University od Stellenbosch [email protected] PP0 PP0 3D Tensor Factorization for Video Restoration A Modified Piecewise Constant Mumford-Shah We have applied blind source separation (BSS) techniques, Model Based Simultaneous Segmentation and Reg- such as independent component analysis and dependent istration component analysis, to video restoration, where the commonly used point spread function (PSF) information in A new variational region based model for a simultaneous blind or non-blind deconvolution is not required. However, image segmentation and registration is proposed. The seg- these matrix factorization based BSS methods have limi- mentation is obtained by minimizing a modified piecewise tations. For instance, image local spatial structure is not constant Mumford-Shah model and registration is assisted used, and constraints should be imposed for unique solu- by the segmentation information and region intensity val- tions. In this paper, we will investigate 3D tensor factor- ues. The numerical experiments of the proposed model are ization for video restoration. It is expected that the quality tested against synthetic data and simulated normal noisy of the restored image will be improved with simpler imple- human-brain magnetic resonance (MR) images. The pre- mentation due to its model-free and constraint-free nature. liminary experimental results show the effectiveness of the IS10 Abstracts 99

The restored image can be further enhanced by formulat- ter object into the process of image formation. Based ing a second multi-channel image restoration problem via on this idea we propose an illumination technique using a Gabor filtering, where 3D tensor factorization is applied projector-camera system that directly displays differences again to achieve final enhancement. between the two objects by projecting an inverse illumination mask of the master object. Qian Du Mississippi State University Robin Gruna [email protected] Karlsruhe Institute of Technology Lehrstuhl für Interaktive Echtzeitsysteme Ivica Kopriva [email protected] Rudjer Bokovic Institute, Zagreb, Croatia [email protected] Jürgen Beyerer Fraunhofer-Institut für Informations- und Datenverarbeitung PP0 [email protected] Synthetic Boundary Conditions and Precondition- ing for Image Deblurring Problems PP0 Given a blurred image and the corresponding blurring op- Shapes from Geometric Measures erator, we try to restore the original unblurred image. We do not use the classical periodic or Neumann boundary In this work we show that shapes can be reconstructed conditions. The boundary conditions we use are directly from simple non asymptotic densities measured only along derived from the blurred images and we name it synthetic edge shapes. The particular density we study corresponds boundary conditions. The resulting deblurred images are to the area of a disk centered on the boundary that is also better than those under classical assumptions. We have inside the shape. It is easy to show uniqueness when these also developed an effective regularized DCT preconditioner densities are known for all radii in a neighborhood of r = to solve these difficult large-scale imaging problems. 0, but much less straightforward when we assume we know it for (almost) only one r ¿ 0. We present variations of Ying Wai Fan uniqueness results for polygons and smooth curves under Emory University certain regularity conditions. [email protected] Sharif Ibrahim,KevinR.Vixie James G. Nagy Washington State University Emory University [email protected], [email protected] Department of Math and Computer Science [email protected] Kevin Sonnanburg Whitworth University [email protected] PP0 A Piecewise Smooth Region Based Simultaneous Image Segmentation and Non-Rigid Registration PP0 A Fully Automated Approach to Segmentation and The goal of the paper is to segment and register novel Registration of Medical Image Data for Pulmonary images simultaneously using a modified piecewise smooth Diagnosis Mumford-Shah technique and region intensity values. The segmentation is obtained by minimizing a modified piece- Molecular imaging is an important tool in drug devel- wise smooth Mumford-Shah model. A non-rigid registra- opment but generates large amounts of data, demand- tion is assisted by the segmentation information and region ing for fully automated analysis tools. We propose a intensity values. The numerical experiments against syn- novel fully-automated approach to the analysis of venti- thetic data and simulated normal noisy human-brain mag- lation/perfusion SPECT data acquired in the context of netic resonance (MR) images show the effectiveness of the pulmonary diseases. Particularly, we propose a modifica- presented model. tion of the Chan-Vese approach for a stable segmentation which then serves as a starting point in a spatial alignment Jung-Ha An process. Our results demonstrate the potential of the new Mathematics Department approach. California State University, Stanislaus [email protected] Alvin I. Ihsani McMaster University Michael Foster Computing and Software California State University Stanislaus [email protected] [email protected] Jan Modersitzki McMaster University PP0 Department of Computing and Software Inverse Illumination Techniques for Automated Vi- [email protected] sual Inspection Troy Farncombe Many industrial inspection tasks can be accomplished by McMaster University comparing a test object with a master object. We review Radiology illumination techniques that aim to minimize the effort of [email protected] defect detection by encoding knowledge about the mas- 100 IS10 Abstracts

PP0 PP0 Texture - Noise Separation Comparing Regularized Cut to Normalized Cut It is a very ill-posed problem to recover a clean image from In comparing two segmentation algorithms approximating a noisy blurred image simply because deblurring and de- the Normalized Cut criterion, both returned reasonable noising processes are contradicting in that deblurring is segmentations for images with simple backgrounds. The sharpening process and denoising is smoothing process. In two algorithms we considered are Hochbaums Normalized this model, we collect some a priori information about pure Cut approximation, which we have called Regularized Cut, noise and pure texture by using different Sobolev spaces of and Shi and Maliks Normalized Cut algorithm. Regular- negative differentiability, which will provide noticeably dif- ized Cut can have more flexibility, since it requires some ferent behaviors, and incorporate them to distinguish noise user interaction, and in practice, Regularized Cut runs from texture. faster than Normalized Cut. Yunho Kim William S. Monroe Department of Mathematics University of Iowa University of California, Irvine [email protected] [email protected] Xiaodong Wu Electrical and Computer Engineering Department PP0 University of Iowa A Variational Joint Framework for Deblurring, De- [email protected] noising and Segmenting.

In this talk, we propose a variational joint framework for Yusung Kim both restoration (deblurring and denoising) and segmenta- Radiation Oncology Department tion of blurred and noisy images. We aim to solve, by an al- University of Iowa ternating framework, an extended modified Mumford-Shah [email protected] functional. The segmentation stage based on the Active Contours Without Edges and solved using Sobolev Gra- PP0 dients and Additive Operator Splitting schemes, allows to partition the image domain into several subdomains. These A Mechanical Bidomain Model of the Heart subdomains are then used to parallelize the computations When representing the electrical properties of the heart of the discretized PDE related to the restoration stage. with the bidomain model, one distinguishes between the Details of the numerical analysis as well as numerical ex- intracellular and extracellular spaces. We develop a bido- periments are provided. main model for the mechanical properties of the heart, Carole Le Guyader accounting for the different mechanical properties inside INSA Rouen, France and outside the cells. This is particularly relevant in cases [email protected] where the intracellular and extracellular (e.g. Lorentz) forces are in opposition. Uses include analysis of displacement of current carrying tissue in MRI. Christian Gout Université de Valenciennes Steffan M. Puwal,BradleyRoth et du Hainaut-Cambrésis Department of Physics [email protected] Oakland University [email protected], [email protected] Isabelle Ramière CEA, France [email protected] PP0 Measuring Conductivity of Biological Tissue Using Magnetic Induction Tomography PP0 Direct Sparse Deblurring Magnetic Induction Tomography is finding use as an experimental tool for mapping the conductivity of biological We propose a deblurring algorithm that explicitly takes tissues. Our numerical approach is to obtain a Fourier ex- into account the sparse characteristics of natural images pansion of the relevant stream functions relating the mag- and does not entail solving a numerically ill-conditioned netic fields, eddy current density, and conductivity (resis- backward-diffusion. The key observation is that the sparse tivity). Thus, we are able to add noise to the system and coefficients that encode a given image with respect to an determine the fidelity of the measured signal to the true over-complete basis are the same that encode a blurred ver- conductivity map. We focus on representations of cardiac sion of the image with respect to a modified basis. Follow- tissue. ing an “analysis-by-synthesis’ approach, an explicit generative model is used to compute a sparse representation of Steffan M. Puwal,BradleyRoth the blurred image, and the coefficients of which are used to Department of Physics combine elements of the original basis to yield a restored Oakland University image. We compare our algorithm against the state of the [email protected], [email protected] art in deblurring algorithms. Yifei Lou PP0 University of California Los Angeles Efficient Implicit Smooothing of Contour Lines for yfl[email protected] IS10 Abstracts 101

Image Reconstruction poral resolution and poor spatial resolution. An EIT- CBCT modality has been investigated in this study. Mo- The standard approach to image reconstruction typically tion information was extracted from EIT images. The mo- produces noisy object boundaries. By contrast to explicit tion data then has been implemented into CBCT recon- edge-field models, we propose to incorporate the smooth- struction for compensating the motion. CT images with ness of the contour lines in an implicit way by introducing reduced motion artefacts could be observed by this dual an additional penalty term defined in the wavelet domain. modality. We also derive an efficient stress-majorization algorithm to solve the associated optimization problem. Our tech- Thanyawee Pengpan nique produces visually pleasing reconstructions which are Department of Electronic and Electrical Engineering, quantitatively better than those obtained without wavelet University of Bath domain constraints. [email protected]

Marc C. Robini Cathryn Mitchell, Manuchehr Soleimani CREATIS Department of Electronic and Electrical Engineering INSA Lyon University of Bath [email protected] [email protected], [email protected] Jean-Philippe Labruyere DePaul University PP0 [email protected] Spatio-Spectral Anomalous Change Detection in Hyperspectral Imagery PP0 Given two images of the same scene, taken at different A Basis Pursuit Approach for Multi-Scale Am-Fm times and under different conditions, the aim of anomalous Reconstructions change detection is to distinguish the pervasive differences (due for instance to illumination or calibration effects) from Recently a new multi-scale amplitude-modulation the actual changes that have occurred in the scene. This frequency-modulation (AM-FM) demodulation method for poster will present an approach for combining local spatial image processing was introduced. The model function con- context with the spectral properties of a pixel for the pur- siders the sum of the product of the instantaneous ampli- pose of identifying anomalous changes in pairs of images. tude (IA) times the cosine of L harmonics of the instantaneous phase (IP) as the independent variables. We propose to consider the L harmonics of the IP as the basis of an James Theiler overcomplete dictionary within the Basis Pursuit frame- Space and Remote Sensing Sciences work. Los Alamos National Laboratory [email protected] Paul Rodriguez Pontifical Catholic University of Peru [email protected] PP0 Graph Based Denoising Victor Murray, Marios Pattichis Using Local Non-Parametric Image Graph Modi- University of New Mexico fications: Variations and Applications [email protected], [email protected] In this work, we describe experiments that explore the recent image denoising and segmentation methods of Asaki PP0 et al. in which minor modifications to the now classical lo- Denoising Using Decomposition cal numerical methods produce good results in cases of low to medium noise. These modifications are based on con- In an earlier work, the author proposed a new decorre- structions of subgraphs of the standard nearest-neighbor lation term to be added to the decomposition model of graph commonly used in numerical computations of gra- Osher, Sole and Vese, with favourable results obtained. In dients. We investigate the precise ways in which the new the present work, the new term is used for the purpose of methods succeed and fail, explaining what we mean by suc- denoising textured images. Time permitting, other new ex- cess and failure. The central feature of the innovation is tensions to decomposition models will also be discussed for the non-parametric nature of the graph modifications. texture denoising. Finally, some applications to real-world imaging will be shown. Thomas Asaki, Keith Clawson, Benjamin Van Dyke, Heather Van Dyke Reza Shahidi Washington State University Memorial University of Newfoundland [email protected], [email protected], [email protected] [email protected], [email protected]

PP0 PP0 Data Fusion of Combined High Spatial Resolution Convolution Equations and Digitization X-Ray CT and High Temporal Resolution Electri- cal Impedance Tomography Imaging The main goal of this paper is approximation of convolution equation on a straight line by a system of linear CBCT is a high spatial resolution imaging system. It suf- algebraic equations in a following way. First given convo- fers from low temporal resolution and consequently from lution kernel one writes out discrete convolution kernel by motion artefacts. EIT can generate images with high tem- direct digitization of continuous kernel, and then the dis- 102 IS10 Abstracts

crete kernel will be cut oﬀ and periodically extended on a within a common context. whole discrete line (so called cyclic convolution). It permits to solve the ﬁnite system of linear algebraic equations Brendt Wohlberg by using fast Fourier transform. Los Alamos National Laboratory [email protected] Vladimir B. Vasilyev Department of Mathematics and Information Technologies PP0 Bryansk State University Hermite Polynomials in a Searching for Global [email protected] Maximum Position

Alexander Vasilyev Analysis of multiextreme functions for maximum is based Department of Physics and Mathematics on the Hermite polynomials series of function symmetrized Bryansk State University around objective (anknown) point. This method searches [email protected] for a global maximum position and in recursive iterations allows to ﬁnd all signiﬁcant maxima.

PP0 Yuriy A. Yatsunenko Fermi National Accelerator Laboratory Small Sample Histograms Variabilty [email protected] Small sample histograms have extreme variabilty as does small-sample-just-about-everything. However for uniform PP0 bin width histograms, extreme shape variability challenges their usefulness. Shape variability can be understood and Logical ”or” in Trajectory Recognition controlled by ﬁrst obtaining all possible shapes via par- Likelyhood function based on logical ”OR” transforms a titioning the space of bin locations and width into shape trajectory recognition (by measured 3D points) in the task level sets. The level sets allow method of moments and of analysis of multi-extreme function of trajectory param- maximum likelihood procedures to be used to obtain rep- eters where each real trajectory corresponds to big maxi- resentative small sample histograms. This builds on J. R. mum at a background of small ones of noise and combina- Thompson’s 1978/1990 histogram maximum likelihood re- torial nature. sult. Yuriy A. Yatsunenko James S. Weber Fermi National Accelerator Laboratory OR and Statistics Consultant [email protected] [email protected]

PP0 Variational Model for Depth from Motion Blur A variational method for combined deblurring and depth estimation from a single still image degraded by spatially variant motion blur is presented. The blur is assumed to be caused by translatory camera motion. The variational method is based on minimising an energy functional with respect to the sharpened image and depth field simultaneously. Experiments on synthetic data confirm the viability of the approach. Steffen Loesch University of Cambridge loeschsteff[email protected]

Martin Welk Mathematical Image Analysis Group Saarland University [email protected]

PP0 Block Estimation Methods in Exemplar-Based Im- age Restoration Exemplar-based methods have recently been shown to give competitive performance in a variety of image restoration tasks, including denoising, inpainting, and super- resolution. One of the most important aspects of an exemplar-based method is the actual block estimation, for which a rather diverse range of algorithms has been applied. We present the results of an extensive set of experiments comparing a number of the leading algorithms