DOCSLIB.ORG

Iterative Reconstruction Methods in MATLAB for Hybrid Inverse Problems in Electrical Impedance Tomography 1

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Iterative Reconstruction Methods in MATLAB for Hybrid Inverse Problems in Electrical Impedance Tomography 1 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 8 February 2021 HyEIT : Iterative Reconstruction Methods in MATLAB for Hybrid Inverse Problems in Electrical Impedance Tomography 1 A.D. Garnadi23a,b, Mokhamad Fakhrul Ulum4d, Deddy Kurniadi51, Utriweni Mukhaiyar6f, Lina Choridah7c, Nurhuda Hendra Setyawan8c, Khusnul Ain9g aInstitute for Globally Distributed Open Research and Education bIPB University, Indonesia cFaculty of Medicine, Public Health, and Nursing Universitas Gadjah Mada, Yogyakarta, Indonesia dFaculty of Veterinary Medicine, IPB University, Indonesia eInstrumentation and Control Research Division, Faculty of Industrial Technology, Institut Teknologi Bandung, Indonesia fStatistics Research Division, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia gFaculty of Sciences and Technology, Airlangga University, Surabaya, Indonesia Abstract We present a MATLAB-based, open source reconstruction software for Hybrid Imaging problem arising from Current Density Impedance Imaging (CDII) and Acoustic-Electrical Impedance Tomography (AEIT), utilizing mixed finite element method solver of Darcy toolbox DarcyLite . For a formulation of hybrid inverse problems in impedance tomography the successive substitution iterative schemes are adapted and an reconstruc- tion algorithm is developed. The problem formulation is a class of hybrid 1Funded by "Riset Kolaborasi Indonesia 2019","Pengembangan Tomografi Elektrik Se- bagai 'Contrasting Agent' Magnetic Resonance Imaging" AND by "Riset Kolaborasi In- donesia 2020", 'Pengembangan Tomografi Hibrida : Electrical Impedance Tomography + Ultrasonography Dalam Bidang Biomedika' 2e-mail address:[email protected] 3home address: Gg Bungur IV 107, Perumahan Cijerah II, Melong, Cimahi Selatan, Indonesia 40534 4e-mail address: [email protected]; OrcID: http://orcid.org/0000-0003-2092-9645 5e-mail address: [email protected] 6e-mail address:[email protected] 7e-mail address: [email protected] 8e-mail address: [email protected] 9e-mail address: k [email protected] Preprint submitted to SoftwareX February 6, 2021 © 2021 by the author(s). Distributed under a Creative Commons CC BY license. Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 8 February 2021 imaging modality which is current density impedance imaging or Acoustic- Electrical Impedance Tomography. The proposed algorithm is implemented numerically in two dimensions. Keywords: Hybrid inverse problems, Iterative reconstruction methods, Impedance tomography, Current density impedance imaging, Magnetic resonance imaging, electrical impedance tomography, Ultrasound modulated electrical impedance tomography Required Metadata Current code version Ancillary data table required for subversion of the codebase. Kindly re- place examples in right column with the correct information about your cur- rent code, and leave the left column as it is. Nr. Code metadata description Please fill in this column C1 Current code version Version 0.0 C2 Permanent link to code/repository NA used for this code version C3 Code Ocean compute capsule C4 Legal Code License CC-BY NC 4.0 International C5 Code versioning system used For example svn, git, mercurial, etc. put none if none C6 Compilation requirements, operat- MATLAB/GNU OCTAVE for the ing future C7 Compilation requirements, operat- DarcyLite ing environments & dependencies http://www.math.colostate.edu/ li- u/DarcyLite.zip C8 If available Link to developer docu- NA mentation/manual C9 Support email for questions agah.garnadi[at]gmail.com Table 1: Code metadata (mandatory) 1 The permanent link to code/repository or the zip archive should include 2 the following requirements: 3 README.txt and LICENSE.txt. 4 Source code in a src/ directory, not the root of the repository. 5 Tag corresponding with the version of the software that is reviewed. 2 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 8 February 2021 6 Documentation in the repository in a docs/ directory, and/or READMEs, 7 as appropriate. 8 1. Motivation and significance 9 In this note we develop and analyse an iterative reconstruction method 10 for the following hybrid inverse problem: 11 12 Reconstruct the scalar function σ from measurements of the form A = σjrujp in Ω; p = 1; 2 (1) 13 where u is the solution to the linear PDE problem r(−σru) = 0 in Ω; (2) uj@Ω = uD; n 14 Here Ω is a smooth open bounded domain in R ; n 2 f2; 3g; and σ is 15 bounded from above and from below by positive constants in Ω: We will 16 henceforth assume that jruj is uniformly bounded from below by a positive 17 constant in Ω: The problem formulation and the reconstruction methods are 18 independent of the spatial dimension, here we only works on n = 2; for pro- 19 totyping. This inverse problem can be identified as a hybrid inverse problem 20 or, equivalently, as a coupled-physics inverse problem, since it models an 21 imaging modality utilizing coupled different physical phenomena. 22 The functions (1) model measurements from a couple of hybrid inverse 23 problems of Electrical Impedance Tomography, i.e. 24 1. In the case p = 1; the functions (1) model measurements of the internal 25 electrical current density and the tomographic method is known as 26 Current Density Impedance Imaging (CDII); the same model appears 27 in certain formulations of Magnetic Resonance Electrical Impedance 28 Tomography (MREIT). [12], [13],[14] 29 2. While for p = 2; coming from AEIT (Acoustics Induce Electric Impedance 30 Tomography). [15], [16] [17], [18] 31 The only package we are aware of with fully fledged capabilities was [21], 32 implemented in PDE suite FENICS, written in C++. 33 2. Software description 34 In this section we derive an iterative reconstruction algorithms for the pre- 35 sented inverse problem. It is common feature of all the presented algorithms, 3 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 8 February 2021 36 that they are based on a transformation of a non-linear problem into a series 37 of linear problems for which the corresponding solutions, under appropriate 38 conditions, converge to a solution to the original non-linear problem. In this 39 section, we explain how to use the successive iterative scheme to reformulate 40 the inverse problem, develop a general iterative reconstruction algorithm and 41 implement it numerically. 42 A way to reformulate (1)-(2) is to recast the set of generalized Laplace 43 problems (2) as non-linear PDE problems. The unknown function σ can be 44 eliminated from the PDEs using the internal measurements, since A σ = ; p = 1; 2: jrujp 45 This gives the non-linear PDE problems r − A ru = 0 in Ω; p = 1; 2; jrujp (3) uj@Ω = uD; 46 In this setting a procedure for solving the inverse problem would be to 47 first solve the non-linear problems for u and then determine σ by (1). One of 48 the simplest approaches to approximate solutions to such a non-linear PDE 49 problem is to use a fixed-point iteration or successive iterative scheme, also 50 known as the method of successive substitutions [4]. The idea behind the 51 successive substitution scheme is basically to make an initial guess on the 52 non-linear coefficient in the PDE problems (3); then the now linear PDE 53 problem is solved, and we get an approximation of u which is used to up- 54 date the estimate of the coefficient. Let the initial guess be denoted by σ0: 55 Throughout this paper, we use a superscript to denote the iteration num- 56 ber. The successive substitution scheme, applied to (3), generates a series of 57 solving linear problems of the type r(−σkruk) = 0 in Ω; k = 0; 1; :::; k (4) u j@Ω = uD; k k+1 58 which are solved successively for (u ): The coefficient σ is defined by 59 the relation A σk+1 = jrukjp 60 It is important to notice that the transformation of the non-linear problem 61 into a series of linear problems is not a result of any algebraic or symbolic 62 manipulations; it simply a consequence of a substitution made directly in the 63 non-linear PDE. The choice of stopping criteria for the successive iterations 64 depends on the application. For problems like ours, where the objective is 4 Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 8 February 2021 65 to estimate the PDE coefficient σ; and not to the functions u; it is natural k+1 k 66 to choose a stopping criteria based on the tolerance kσ − σ k in some 67 suitable function space and the iteration number k: 68 The performance of the successive substitution relies on an initial guess 69 that provides a sufficiently good starting point, such that the successive ap- 70 proximation of the nonlinear coefficients is improved in each iteration. The 71 convergence properties of the successive substitution scheme can be studied 72 using contraction maps and the application of the Banach fixed point theo- 73 rem, however the practicality of applying this theory on a general non-linear 74 PDE problem seems rather limited [4]. Nonetheless, for our case, the con- 75 vergence properties of the successive substitution have been analysed [2, 6]. 76 The successive substitution scheme was the main idea behind one of the 77 first reconstruction algorithms for the hybrid inverse problems expressed in 78 the form of the non-linear PDE problems given by (3). The resulting al- 79 gorithm was denoted the J-substitution algorithm, due to the fact that the 80 functions A models measurements of the magnitude of the current density 81 vector field, often denoted by A [3]. Note that the original formulation of 82 the J-substitution algorithm considered the corresponding Neumann prob- 83 lem. A similar implementation of the Dirichlet problem for a single internal 84 measurement has also been used to solve the equivalent inverse problem from 85 CDII [5, 6]. 86 2.1. Software Architecture 87 The successive iterative scheme can be applied directly to the non-linear 88 PDE formulation of the inverse problem to produce the following algorithm: 89 - Algorithm.
Load more

Recommended publications
  • Optimizing-Oncologic-FDG-PET-CT
    Optimizing Oncologic FDG-PET/CT Scans to Decrease Radiation Exposure Esma A. Akin, MD George Washington University Medical Center, Washington, DC Drew A. Torigian, MD, MA University of Pennsylvania Medical Center, Philadelphia, PA Patrick M. Colletti, MD University of Southern California Medical Center, Los Angeles, CA Don C. Yoo, MD The Warren Alpert Medical School of Brown University, Providence, RI (Updated: April 2017) The development of dual-modality positron emission tomography/computed tomography (PET/CT) systems with near-simultaneous acquisition capability has addressed the limited spatial resolution of PET and has improved accurate anatomical localization of sites of radiotracer uptake detected on PET. PET/CT also allows for CT-based attenuation correction of the emission scan without the need for an external positron-emitting source for a transmission scan. This not only addresses the limitations of the use of noisy transmission data, therefore improving the quality of the attenuation-corrected emission scan, but also significantly decreases scanning time. However, this comes at the expense of increased radiation dose to the patient compared to either PET or CT alone. Optimizing PET protocols The radiation dose results both from the injected radiotracer 18F-2-fluoro-2-deoxy-D-glucose (FDG), which is ~7 mSv from an injected dose of 10 mCi (given the effective dose of 0.019 mSv/MBq (0.070 rem/mCi) for FDG), as well as from the external dose of the CT component, which can run as high as 25 mSv [1]. This brings the total dose of FDG-PET/CT to a range of ~8 mSv up to 30 mSv, depending on the type of study performed as well as the anatomical region and number of body parts imaged, although several recent studies have reported a typical average dose of ~14 mSv for skull base-to-thigh FDG- PET/CT examinations [2-8].
    [Show full text]
  • Highly Scalable Image Reconstruction Using Deep Neural Networks with Bandpass Filtering Joseph Y
    1 Highly Scalable Image Reconstruction using Deep Neural Networks with Bandpass Filtering Joseph Y. Cheng, Feiyu Chen, Marcus T. Alley, John M. Pauly, Member, IEEE, and Shreyas S. Vasanawala Abstract—To increase the flexibility and scalability of deep high-density receiver coil arrays for “parallel imaging” [2]– neural networks for image reconstruction, a framework is pro- [6]. Also, image sparsity can be leveraged to constrain the posed based on bandpass filtering. For many applications, sensing reconstruction problem for compressed sensing [7]–[9]. With measurements are performed indirectly. For example, in magnetic resonance imaging, data are sampled in the frequency domain. the use of nonlinear sparsity priors, these reconstructions are The introduction of bandpass filtering enables leveraging known performed using iterative solvers [10]–[12]. Though effective, imaging physics while ensuring that the final reconstruction is these algorithms are time consuming and are sensitive to consistent with actual measurements to maintain reconstruction tuning parameters which limit their clinical utility. accuracy. We demonstrate this flexible architecture for recon- We propose to use CNNs for image reconstruction from structing subsampled datasets of MRI scans. The resulting high subsampling rates increase the speed of MRI acquisitions and subsampled acquisitions in the spatial-frequency domain, and enable the visualization rapid hemodynamics. transform this approach to become more tractable through the use of bandpass filtering. The goal of this work is to enable Index Terms—Magnetic resonance imaging (MRI), Compres- sive sensing, Image reconstruction - iterative methods, Machine an additional degree of freedom in optimizing the computation learning, Image enhancement/restoration(noise and artifact re- speed of reconstruction algorithms without compromising re- duction).
    [Show full text]
  • Arxiv:1707.05927V1 [Physics.Med-Ph] 19 Jul 2017
    Medical image reconstruction: a brief overview of past milestones and future directions Jeffrey A. Fessler University of Michigan July 20, 2017 At ICASSP 2017, I participated in a panel on “Open Problems in Signal Processing” led by Yonina Eldar and Alfred Hero. Afterwards the editors of the IEEE Signal Processing Magazine asked us to write a “perspectives” column on this topic. I prepared the text below but later found out that equations or citations are not the norm in such columns. Because I had already gone to the trouble to draft this version with citations, I decided to post it on arXiv in case it is useful for others. Medical image reconstruction is the process of forming interpretable images from the raw data recorded by an imaging system. Image reconstruction is an important example of an inverse problem where one wants to determine the input to a system given the system output. The following diagram illustrates the data flow in an medical imaging system. Image Object System Data Images Image −−−−−→ −−−→ reconstruction −−−−−→ → ? x (sensor) y xˆ processing (estimator) Until recently, there have been two primary methods for image reconstruction: analytical and iterative. Analytical methods for image reconstruction use idealized mathematical models for the imaging system. Classical examples are the filtered back- projection method for tomography [1–3] and the inverse Fourier transform used in magnetic resonance imaging (MRI) [4]. Typically these methods consider only the geometry and sampling properties of the imaging system, and ignore the details of the system physics and measurement noise. These reconstruction methods have been used extensively because they require modest computation.
    [Show full text]
  • Positron Emission Tomography with Three-Dimensional Reconstruction
    SE9700024 Positron Emission Tomography with Three-dimensional reconstruction Kjell Erlandsson Radiation Physics Department The Jubileum Institute Lund University Sweden 1996 Doctoral Dissertation 1996 Radiation Physics Department The Jubileum Institute Lund University Printed in Sweden by KF-Sigma, Lund, 1996 ISBN 91-628-2189-X Copyright © Kjell Erlandsson (pages 1-67) All rights reserved "I'm guided by the beauty of our weapons." Leonard Cohen LIST OF ORIGINAL PAPERS This thesis is based on the following papers, which will be referred to in the text by their Roman numerals: I. Sandell A, Erlandsson K, Ohlsson T, Strand S-E, "A PET Scanner Based on Rotating Scintillation Cameras: Development and Experience", submitted to J Nucl Med, 1996. II. Erlandsson K, Strand S-E, "A New Approach to Three-Dimensional Image Reconstruction in PET", IEEE Trans Nucl Sci, 39:1438-1443, 1992. III. Erlandsson K, Esser PD, Strand S-E, van Heertum RL, "3D Reconstruction for a Multi-Ring PET Scanner by Single-Slice Rebinning and Axial Deconvolution", Phys Med Biol, 39:619-629, 1994. IV. Erlandsson K, Strand S-E, "3D Reconstruction for 2D PET", submitted to Nucl Instr Meth A, 1996. V. Sandell A, Erlandsson K, Bertenstam L, "A Scanner for Positron Emission Mammography", submitted to Phys Med Biol, 1996. ABSTRACT In this thesis, the developments of two different low-cost scanners for positron emission tomography (PET), based on 3D acquisition, are presented. 3D reconstruction methods for these systems were also developed. The first scanner consists of two rotating scintillation cameras, and produces quantitative images, which have shown to be clinically useful.
    [Show full text]
  • Comparison Among Tomographic Reconstruction Algorithms with a Limited Data
    2011 International Nuclear Atlantic Conference - INAC 2011 Belo Horizonte,MG, Brazil, October 24-28, 2011 Associação Brasileira de Energia Nuclear - ABEN ISBN: 978-85-99141-04-5 COMPARISON AMONG TOMOGRAPHIC RECONSTRUCTION ALGORITHMS WITH A LIMITED DATA Eric F. Oliveira1, Sílvio B. Melo2, Carlos C. Dantas3, Daniel A. A. Vasconcelos4 and Luís F. Cadiz5 1Department of Nuclear Energy -DEN Federal University of Pernambuco – UFPE, Av. Prof. Luiz Freire 1000, CDU 50740-540 Recife, PE, Brazil [email protected] 2Informatic Center - CIN Federal University of Pernambuco – UFPE Av. Prof. Luiz Freire 1000 CDU 50740-540 Recife, PE, Brazil [email protected] 3 Department of Nuclear Energy -DEN Federal University of Pernambuco – UFPE, Av. Prof. Luiz Freire 1000, CDU 50740-540 Recife, PE, Brazil [email protected] 4Department of Nuclear Energy -DEN Federal University of Pernambuco – UFPE, Av. Prof. Luiz Freire 1000, CDU 50740-540 Recife, PE, Brazil [email protected] 5Department of Nuclear Energy -DEN Federal University of Pernambuco – UFPE, Av. Prof. Luiz Freire 1000, CDU 50740-540 Recife, PE, Brazil [email protected] ABSTRACT Nowadays there is a continuing interest in applying computed tomography (CT) techniques in non-destructive testing and inspection of many industrial products. These applications of CT usually require a differentiated analysis when there are strong limitations in acquiring a sufficiently large amount of projection data. The use of a low number of tomographic data normally degrades the quality of the reconstructed image, highlighting the formation of artifacts and noise. This work investigates the reconstruction methods most commonly used (FBP, ART, SIRT, MART, SMART) and shows the performance of each one in this limited scenario.
    [Show full text]
  • Deep Learning CT Image Reconstruction in Clinical Practice CT-Bildrekonstruktion Mit Deep Learning in Der Klinischen Praxis
    Published online: 2020-12-10 Review Deep Learning CT Image Reconstruction in Clinical Practice CT-Bildrekonstruktion mit Deep Learning in der klinischen Praxis Authors Clemens Arndt, Felix Güttler, Andreas Heinrich, Florian Bürckenmeyer, Ioannis Diamantis, Ulf Teichgräber Affiliation Ergebnis und Schlussfolgerung DL als Methode des Ma- Department of Radiology, Jena University Hospital, Jena, chine Learning nutzt im Allgemeinen ein trainiertes, künstli- Germany ches, neuronales Netzwerk zur Lösung von Problemen. Ak- tuell sind DL-Rekonstruktionsalgorithmen von 2 Herstellern Key words für die klinische Routine verfügbar. In den bisherigen Studien computed tomography, image reconstruction, deep neural konnte eine Reduktion des Bildrauschens und eine Verbesser- network, deep learning, artificial intelligence, image ung der Gesamtqualität gezeigt werden. Eine Studie zeigte, denoising bei höherer Qualität der mittels DL rekonstruierten Bilder, received 11.05.2020 eine vergleichbare diagnostische Genauigkeit zur IR für die accepted 20.08.2020 Detektion von Koronarstenosen. Weitere Studien sind not- published online 10.12.2020 wendig und sollten vor allem auch auf eine klinische Überle- genheit abzielen, während dabei ein breiter Umfang an Patho- Bibliography logien umfasst werden muss. Fortschr Röntgenstr 2021; 193: 252–261 DOI 10.1055/a-1248-2556 Kernaussagen: ▪ ISSN 1438-9029 Nach der aktuell verbreiteten iterativen Rekonstruktion © 2020. Thieme. All rights reserved. können CT-Schnittbilder im klinischen Alltag nun auch Georg Thieme Verlag KG, Rüdigerstraße 14, mittels Deep Learning (DL) als Methode der künstlichen 70469 Stuttgart, Germany Intelligenz rekonstruiert werden. ▪ Durch DL-Rekonstruktionen können Bildrauschen vermin- Correspondence dert, Bildqualität verbessert und möglicherweise Strah- Dr. Clemens Arndt lung reduziert werden. Institut für Diagnostische und Interventionelle Radiologie, ▪ Eine diagnostische Überlegenheit im klinischen Kontext Universitätsklinikum Jena, Am Klinikum 1, 07751 Jena, sollte in kommenden Studien gezeigt werden.
    [Show full text]
  • Image Reconstruction for PET/CT Scanners: Past Achievements and Future Challenges
    REVIEW Image reconstruction for PET/CT scanners: past achievements and future challenges PET is a medical imaging modality with proven clinical value for disease diagnosis and treatment monitoring. The integration of PET and CT on modern scanners provides a synergy of the two imaging modalities. Through different mathematical algorithms, PET data can be reconstructed into the spatial distribution of the injected radiotracer. With dynamic imaging, kinetic parameters of specific biological processes can also be determined. Numerous efforts have been devoted to the development of PET image reconstruction methods over the last four decades, encompassing analytic and iterative reconstruction methods. This article provides an overview of the commonly used methods. Current challenges in PET image reconstruction include more accurate quantitation, TOF imaging, system modeling, motion correction and dynamic reconstruction. Advances in these aspects could enhance the use of PET/CT imaging in patient care and in clinical research studies of pathophysiology and therapeutic interventions. 1 K EYWORDS: analytic reconstruction fully 3D imaging iterative reconstruction Shan Tong , maximum-likelihood expectation-maximization method PET Adam M Alessio1 & Paul E Kinahan†1 PET is a medical imaging modality with proven 1Department of Radiology, University clinical value for the detection, staging and PET tomographic data of Washington, Seattle WA, USA †Author for correspondence: monitoring of a wide variety of diseases. This Problem statement Tel.: +1 206 543 0236 technique requires the injection of a radiotracer, Data acquisition & representation Fax: +1 206 543 8356 which is then monitored externally to generate PET imaging can measure the spatial distribu- [email protected] PET data [1,2].
    [Show full text]
  • UCLA Electronic Theses and Dissertations
    UCLA UCLA Electronic Theses and Dissertations Title New Algorithms in Computational Microscopy Permalink https://escholarship.org/uc/item/1r48b4mg Author Pham, Minh Publication Date 2020 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California UNIVERSITY OF CALIFORNIA Los Angeles New Algorithms in Computational Microscopy A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Mathematics by Minh Pham 2020 © Copyright by Minh Pham 2020 ABSTRACT OF THE DISSERTATION New Algorithms in Computational Microscopy by Minh Pham Doctor of Philosophy in Mathematics University of California, Los Angeles, 2020 Professor Stanley Osher, Chair Microscopy plays an important role in providing tools to microscopically observe objects and their surrounding areas with much higher resolution ranging from the scale between molecular machineries (angstrom) and individual cells (micrometer). Under microscopes, illumination, such as visible light and electron-magnetic radiation/electron beam, interacts with samples, then they are scattered to a plane and are recorded. Computational mi- croscopy corresponds to image reconstruction from these measurements as well as improving quality of the images. Along with the evolution of microscopy, new studies are discovered and algorithms need development not only to provide high-resolution imaging but also to decipher new and advanced researches. In this dissertation, we focus on algorithm development for inverse
    [Show full text]
  • Iterative PET Image Reconstruction Using Convolutional Neural
    1 Iterative PET Image Reconstruction Using Convolutional Neural Network Representation Kuang Gong, Jiahui Guan, Kyungsang Kim, Xuezhu Zhang, Georges El Fakhri, Jinyi Qi* and Quanzheng Li* Abstract—PET image reconstruction is challenging due to temporal information. Denoising methods, such as the HYPR the ill-poseness of the inverse problem and limited number of processing [9], non-local mean denoising [10], [11] and guided detected photons. Recently deep neural networks have been image filtering [12] have been developed and show better widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this work, we performance in bias-variance tradeoff or partial volume cor- trained a deep residual convolutional neural network to improve rection than the conventional Gaussian filtering. In regularized PET image quality by using the existing inter-patient information. image reconstruction, entropy or mutual information based An innovative feature of the proposed method is that we embed methods [13]–[15], segmentation based methods [16], [17], the neural network in the iterative reconstruction framework for and gradient based methods [18], [19] have been developed image representation, rather than using it as a post-processing tool. We formulate the objective function as a constraint op- by penalizing the difference between the reconstructed image timization problem and solve it using the alternating direction and the prior information in specific domains. The Bowsher’s method of multipliers (ADMM) algorithm. Both simulation data method [20] adjusts the weight of the penalty based on and hybrid real data are used to evaluate the proposed method. similarity metrics calculated from prior images.
    [Show full text]
  • A New Era of Image Reconstruction: Truefidelity™
    A new era of image reconstruction: TrueFidelity™ Technical white paper on deep learning image reconstruction Jiang Hsieh, Eugene Liu, Brian Nett, Jie Tang, Jean-Baptiste Thibault, Sonia Sahney Contents 02 Introduction 02 Challenges of Filtered Back-Projection and Iterative Reconstruction 03 The New Era of Deep Learning-Based Image Reconstruction 07 Early Evidence: Phantom Studies 10 Early Evidence: Clinical Cases 13 Conclusion 14 Glossary and References gehealthcare.com Introduction GE Healthcare’s deep learning image reconstruction (DLIR) is the first outstanding image quality and preferred noise texture, have the potential Food and Drug Administration (FDA) cleared technology to utilize a deep to improve reading confidence in a wide range of clinical applications, neural network-based recon engine to generate high quality TrueFidelity including imaging the head, whole body, cardiovascular, and for patients computed tomography (CT) images. DLIR opens a new era for CT-image of all ages. DLIR is designed with fast reconstruction speed for routine reconstruction by addressing challenges of filtered back-projection (FBP) CT use, even in acute care settings. and iterative reconstruction (IR). This white paper will: first, take a look at the overall evolution of CT DLIR features a deep neural network (DNN), which was trained with high image reconstruction; second, explain the design, supervised training, and quality FBP data sets to learn how to differentiate noise from signals, deployment of DLIR engine; and third, reveal early phantom and
    [Show full text]
  • Iterative PET Image Reconstruction Using CNN Representation
    This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMI.2018.2869871, IEEE Transactions on Medical Imaging 1 Iterative PET Image Reconstruction Using Convolutional Neural Network Representation Kuang Gong, Jiahui Guan, Kyungsang Kim, Xuezhu Zhang, Jaewon Yang, Youngho Seo, Georges El Fakhri, Jinyi Qi* and Quanzheng Li* Abstract—PET image reconstruction is challenging due to can be used to take various degradation factors into consid- the ill-poseness of the inverse problem and limited number of eration [8]. In addition, various post processing approaches detected photons. Recently deep neural networks have been and iterative reconstruction methods have been developed widely and successfully used in computer vision tasks and attracted growing interests in medical imaging. In this work, we by making use of local patch statistics, prior anatomical or trained a deep residual convolutional neural network to improve temporal information. Denoising methods, such as the HYPR PET image quality by using the existing inter-patient information. processing [9], non-local mean denoising [10], [11] and guided An innovative feature of the proposed method is that we embed image filtering [12] have been developed and show better the neural network in the iterative reconstruction framework for performance in bias-variance tradeoff or partial volume cor- image representation, rather than using it as a post-processing tool. We formulate the objective function as a constrained rection than the conventional Gaussian filtering. In regularized optimization problem and solve it using the alternating direction image reconstruction, entropy or mutual information based method of multipliers (ADMM) algorithm.
    [Show full text]
  • Distributed Computation of Linear Inverse Problems with Application to Computed Tomography Reconstruction Yushan Gao, Thomas Blumensath
    1 Distributed Computation of Linear Inverse Problems with Application to Computed Tomography Reconstruction Yushan Gao, Thomas Blumensath, Abstract—The inversion of linear systems is a fundamental step where y; A; x and e are projection data, system matrix, re- in many inverse problems. Computational challenges exist when constructed image vector and measurement noise respectively. trying to invert large linear systems, where limited computing However, the relatively lower computational efficiency limits resources mean that only part of the system can be kept in computer memory at any one time. We are here motivated their use, especially in many x-ray tomography problems, by tomographic inversion problems that often lead to linear where y and x can have millions of entries each [9] and inverse problems. In state of the art x-ray systems, even a where A, even though it is a sparse matrix, can have billions standard scan can produce 4 million individual measurements of entries. and the reconstruction of x-ray attenuation profiles typically For realistic dataset sizes, these methods thus require sig- requires the estimation of a million attenuation coefficients. To deal with the large data sets encountered in real applications nificant computational resources, especially as the matrix A and to utilise modern graphics processing unit (GPU) based is seldom kept in memory but is instead re-computed on the computing architectures, combinations of iterative reconstruction fly, which can be done relatively efficiently using the latest algorithms and parallel computing schemes are increasingly Graphical Processor Unit (GPU) based parallel computing applied. Although both row and column action methods have platforms.
    [Show full text]