32 IS06 Abstracts

CP1 lem from Surface Measurements Adaptive Finite Element Methods for Inverse Imaging Problems Assuming that the heat capacity of a body is negligible outside certain inclusions the heat equation degenerates to In many realistic 3d imaging problems, such as biomedical a parabolic-elliptic interface problem. For the case that the tumor diagnostics or underground imaging, the resolution heat conductivity is higher inside the inclusions we show by requested by practitioners is unachiavable using globally an adaptation of the so-called Factorization Method that refined meshes. However, while now the leading paradigm the locations of the interfaces are uniquely determined by in PDE solvers, adaptivity has not been widely used for thermal measurements on the surface of the body. We also inverse problems. We will present a mathematical frame- present some numerical results for this inverse problem. work for imaging applications using automatically adapted meshes, and present results obtained in optical tomography Otmar Scherzer for tumor detection and sound wave imaging applications. University Innsbruck [email protected] Wolfgang Bangerth Texas A&M University Bastian Gebauer [email protected] Institut f¨ur Mathematik, Joh. Gutenberg-Universit¨at Mainz, Germany [email protected] CP1 A New Approach to Inverse Problem Solving Using Florian Fr¨uhauf Radon-Based Representations Department of Computer Science, University of Innsbruck, Austria We carry out image deconvolution by transforming the fl[email protected] data into a new general discrete Radon domain that can handle any assumed boundary condition for the associ- ated matrix inversion problem. For each associated angular CP1 segment, one can apply deconvolution routines to smaller A Threshold-Based Method for Inverse Solutions (and possibly better) conditioned matrix inversion prob- to Reconstruct Complex Obstacles, with Applica- lems than the matrix inversion problem for the entire im- tion to the Inverse Problem of Electrocardiography age. We then devise methods for doing this scheme locally to provide estimates based on a multi-scaled representa- Inspired by the inverse problem of electrocardiography, we tion. introduce a method to reconstruct a two-level image or im- age sequence with multiple objects and complex transition Glenn Easley regions. We construct a first, two-level estimate of the so- Systems Planning Corporation lution (here, heart potentials) using an adaptive threshold- [email protected] based boundary, which becomes a constraint for a second, Tikhonov regularized, estimate. We iterate (recursively or Dennis Healy in time) between the two estimates. Simulation results us- DARPA/DSO ing measured canine data show considerable improvement [email protected] over standard Tikhonov solutions.

Carlos Berenstein Gealid Tadmor University of Maryland Northeastern University [email protected] [email protected]

Rob MacLeod CP1 University of Utah Multiscale Formation Imaging Using Array Resis- SCI, CVRTI, and Bioengineering Dept tivity Logging Data [email protected]

Existing log interpretation methods use a single model. Alireza Ghodrati Such an approach does not allow fully extracting infor- Northeastern University mation from the recorded logs. Our imaging method uses [email protected] a set of log-resolution-dependent models designed for array tools possessing different vertical resolution and depth of investigation. We generate an image using coarse models, Dana H. Brooks inverting the logs with the lowest resolution. We then per- Northeastern University form iterative image refining using multiscale models. The Dept. of Electrical and Computer Engineering method reconstructs the borehole’s surrounding features [email protected] clearly and quantitatively. Michael A. Frenkel CP1 Baker Hughes, Houston Technology Center Electron Microscope Tomography: Calculating and [email protected] Inverting the Generalized Ray Transfor