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Wang, Jing

A two-step accelerated Landweber-type iteration regularization algorithm for sparse reconstruction of electrical impedance tomography. (English) Zbl 07861196

Math. Methods Appl. Sci. 47, No. 5, 3261-3272 (2024).

Cited in 1 Document

MSC:

92C55 Biomedical imaging and signal processing
65J22 Numerical solution to inverse problems in abstract spaces
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs

Keywords:

electrical impedance tomography; image reconstruction; iteration regularization; two-step Landweber-type iteration
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Full Text: DOI

References:

[1] CheneyM, IsaacsonD, NewellJC. Electrical impedance tomography. SIAM Rev. 1999;41:85‐101. · Zbl 0927.35130
[2] BorceaL. Electrical impedance tomography. Inverse Probl. 2002;18:99‐136. · Zbl 1031.35147
[3] BrownBH. Electrical impedance tomography (EIT): A review. J Med Eng Technol. 2003;27(3):97‐108.
[4] LionheartWRB. EIT Reconstruction algorithms: pitfalls, challenges and recent developments. Physiol Measurement. 2004;25(1):125‐142.
[5] AbdelsalamSI, ZaherAZ. Leveraging elasticity to uncover the role of rabinowitsch suspension through a wavelike conduit: Consolidated blood suspension application. Mathematics. 2021;9(16):2008.
[6] SantosaF, VogeliusM. A backprojection algorithm for electrical impedance imaging. SIAM J Appl Math. 1990;50(1):216‐243. · Zbl 0691.65087
[7] LohWW, DickinFJ. Improved modified Newton‐Raphson algorithm for electrical impedance tomography. Electron Lett. 1996;32(3):206‐207.
[8] VauhkonenM, VadaszD. Tikhonov regularization and prior information in electrical impedance tomography. IEEE Trans Med Imaging. 1998;17(2):285‐93.
[9] BorsicA, GrahamBM, AdlerA, et al. In vivo impedance imaging with total variation regularization. IEEE Trans Med Imaging. 2010;29(1):44‐54.
[10] JinB, KhanT, MaassP. A reconstruction algorithm for electrical impedance tomography based on sparsity regularization. Int J Numer Methods Eng. 2012;89(3):337‐353. · Zbl 1242.78016
[11] WangJ, MaJ, HanB, et al. Split Bregman iterative algorithm for sparse reconstruction of electrical impedance tomography. Signal Process. 2012;92(12):2952‐2961.
[12] PhamMQ. Reconstructing conductivity coefficients based on sparsity regularization and measured data in electrical impedance tomography. Inverse Probl Sci Eng. 2015;23(8):1366‐1387. · Zbl 1326.92048
[13] GardeH, KnudsenK. Sparsity prior for electrical impedance tomography with partial data. Inverse Probl Sci Eng. 2016;24(3):524‐541.
[14] YangYJ, JiaJB. An image reconstruction algorithm for electrical impedance tomography using adaptive group sparsity constraint. IEEE Trans Instrument Measure. 2017;66(9):2295‐2305.
[15] LiJ, YueSH, DingM, et al. Adaptive Lp regularization for electrical impedance tomography. IEEE Sensors J. 2019;19(24):12297‐12305.
[16] WangJ, HanB, WangW. Elastic‐net regularization for nonlinear electrical impedance tomography with a splitting approach. Applicable Anal. 2019;98(12):2201‐2217. · Zbl 1418.65056
[17] HuskaM, LazzaroD, MorigiS, et al. Spatially‐adaptive variational reconstructions for linear inverse electrical impedance tomography.J Sci Comput. 2020;84(3):46. · Zbl 07246751
[18] ShiY, KongX, WangM, et al. A non‐convex L1‐norm penalty‐based total generalized variation model for reconstruction of conductivity distribution. IEEE Sensors J. 2020;20(14):8137‐8146.
[19] WangJ. Non‐convex Lp regularization for sparse reconstruction of electrical impedance tomography. Inverse Probl Sci Eng. 2021;29(7):1032‐1053. · Zbl 1472.35369
[20] WangH, ChaoW, YinW. A pre‐iteration method for the inverse problem in electrical impedance tomography. IEEE Trans Instrument Measurement. 2004;53(4):1093‐1096.
[21] KimBS, KimJH, KimS, et al. Image reconstruction using modified iterative Landweber method in electrical impedance tomography. Syst Control. 2012;49(4):36‐44.
[22] KimBS, KimS, KimKY. Development of novel on‐line Landweber algorithm for image reconstruction in electrical impedance tomography. J Inst Electron Inform Eng. 2012;49(9):293‐298.
[23] WangJ, HanB. Image reconstruction based on homotopy perturbation inversion method for electrical impedance tomography. J Appl Math. 2013;2013(11):135‐148. · Zbl 1397.65241
[24] YeJ, WangH, YangW. A sparsity reconstruction algorithm for electrical capacitance tomography based on modified Landweber iteration. Measurement Sci Technol. 2014;25(11):115402.
[25] KimBS, KimKY. Resistivity imaging of binary mixture using weighted Landweber method in electrical impedance tomography. Flow Meas Instrum. 2017;53:39‐48.
[26] WangJ, HanB. Application of a class of iterative algorithms and their accelerations to Jacobian‐based linearized EIT image reconstruction. Inverse Probl Sci Eng. 2021;29(8):1108‐1126. · Zbl 1471.94005
[27] LiuS, JiaJ, ZhangYD, et al. Image reconstruction in electrical impedance tomography based on structure‐aware sparse Bayesian learning. IEEE Trans Med Imaging. 2018;37(9):2090‐2102.
[28] AhmadS, StraussT, KupisS, et al. Comparison of statistical inversion with iteratively regularized Gauss Newton method for image reconstruction in electrical impedance tomography. Appl Math Comput. 2019;358(1):436‐448. · Zbl 1428.78036
[29] FanYW, YingLX. Solving electrical impedance tomography with deep learning. J Comput Phys. 2019;404:109119. · Zbl 1453.65041
[30] LiuD, SmylD, DuJ. A parametric level set‐based approach to difference imaging in electrical impedance tomography. IEEE Trans Med Imaging. 2019;38(1):145‐155.
[31] LiuD, GuD, SmylD, et al. B‐spline level set method for shape reconstruction in electrical impedance tomography. IEEE Trans Med Imaging. 2020;39(6):1917‐1929.
[32] Fernandez‐FuentesX, MeraD, GomezA, et al. Towards a fast and accurate EIT inverse problem solver: a machine learning approach. Electronics. 2018;7(12):422.
[33] SymlD, LiuD. Optimizing electrode positions in 2‐D electrical impedance tomography using deep learning. IEEE Trans Instrument Measurement. 2020;69(9):6030‐6044.
[34] MartinsT, SatoAK, MouraF, et al. A review of electrical impedance tomography in lung applications: Theory and algorithms for absolute images. Ann Rev Control. 2019;48:442‐471.
[35] KhanTA, LingSH. Review on electrical impedance tomography: artificial intelligence methods and its applications. Algorithms. 2019;12(5):88. · Zbl 1461.94011
[36] LandweberL. An iteration formula for Fredholm integral equations of the first kind. Am J Math. 1951;73(3):615‐624. · Zbl 0043.10602
[37] SomersaloE, CheneyM, IsaacsonD. Existence and uniqueness for electrode models for electric current computed tomography. SIAM J Appl Math. 1992;52(4):1023‐1040. · Zbl 0759.35055
[38] VauhkonenM, KaipioJP, SomersaloE, et al. Electrical impedance tomography with basis constraints. Inverse Probl. 1997;13(2):523‐530. · Zbl 0872.35130
[39] WooEJ, HuaP, WebsterJG, et al. Finite‐element method in electrical impedance tomography. Med Biol Eng Comput. 1994;32(5):530‐536.
[40] YorkeyTJ, WebsterJG, TompkinsWJ. Comparing reconstruction algorithms for electrical impedance tomography. IEEE Trans Biomed Eng. 1987;34(11):843‐852.
[41] ScherzerO. A convergence analysis of a method of steepest descent and a two‐step algorithm for nonlinear ill‐posed problems. Numer Funct Anal Optim. 1996;17(1‐2):197‐214. · Zbl 0852.65048
[42] BotRI, HeinT. Iterative regularization with a general penalty term-theory and application to L^1 and TV regularization. Inverse Probl. 2012;28(10):104010. · Zbl 1269.47054
[43] NesterovY. A method of solving a convex programming problem with convergence rate O(1/K^2). Soviet Math Doklady. 1983;27:372‐376. · Zbl 0535.90071
[44] NeubauerA. On Nesterov acceleration for Landweber iteration of linear ill‐posed problems. J Inverse Ill‐Posed Probl. 2017;25(3):381‐390. · Zbl 1367.47017
[45] VauhkonenM, LionheartWR, HeikkinenLM, et al. A MATLAB package for the EIDORS project to reconstruct two‐dimensional EIT images. Physiol Meas. 2001;22(1):107‐111.
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