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Kaczmarz methods for regularizing nonlinear ill-posed equations I: convergence analysis
Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography
1. | Institute of Mathematics, Helsinki University of Technology, FI-02015 HUT, Finland, Finland, Finland |
[1] |
Hiroshi Isozaki. Inverse boundary value problems in the horosphere - A link between hyperbolic geometry and electrical impedance tomography. Inverse Problems and Imaging, 2007, 1 (1) : 107-134. doi: 10.3934/ipi.2007.1.107 |
[2] |
Bastian Gebauer, Nuutti Hyvönen. Factorization method and inclusions of mixed type in an inverse elliptic boundary value problem. Inverse Problems and Imaging, 2008, 2 (3) : 355-372. doi: 10.3934/ipi.2008.2.355 |
[3] |
Fabrice Delbary, Rainer Kress. Electrical impedance tomography using a point electrode inverse scheme for complete electrode data. Inverse Problems and Imaging, 2011, 5 (2) : 355-369. doi: 10.3934/ipi.2011.5.355 |
[4] |
Erfang Ma. Integral formulation of the complete electrode model of electrical impedance tomography. Inverse Problems and Imaging, 2020, 14 (2) : 385-398. doi: 10.3934/ipi.2020017 |
[5] |
Jérémi Dardé, Harri Hakula, Nuutti Hyvönen, Stratos Staboulis. Fine-tuning electrode information in electrical impedance tomography. Inverse Problems and Imaging, 2012, 6 (3) : 399-421. doi: 10.3934/ipi.2012.6.399 |
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Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, Jari P. Kaipio, Erkki Somersalo. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part II: Stochastic extension of the boundary map. Inverse Problems and Imaging, 2015, 9 (3) : 767-789. doi: 10.3934/ipi.2015.9.767 |
[7] |
Ville Kolehmainen, Matti Lassas, Petri Ola, Samuli Siltanen. Recovering boundary shape and conductivity in electrical impedance tomography. Inverse Problems and Imaging, 2013, 7 (1) : 217-242. doi: 10.3934/ipi.2013.7.217 |
[8] |
Melody Alsaker, Sarah Jane Hamilton, Andreas Hauptmann. A direct D-bar method for partial boundary data electrical impedance tomography with a priori information. Inverse Problems and Imaging, 2017, 11 (3) : 427-454. doi: 10.3934/ipi.2017020 |
[9] |
Yosra Boukari, Houssem Haddar. The factorization method applied to cracks with impedance boundary conditions. Inverse Problems and Imaging, 2013, 7 (4) : 1123-1138. doi: 10.3934/ipi.2013.7.1123 |
[10] |
Gen Nakamura, Päivi Ronkanen, Samuli Siltanen, Kazumi Tanuma. Recovering conductivity at the boundary in three-dimensional electrical impedance tomography. Inverse Problems and Imaging, 2011, 5 (2) : 485-510. doi: 10.3934/ipi.2011.5.485 |
[11] |
Ke Zhang, Maokun Li, Fan Yang, Shenheng Xu, Aria Abubakar. Electrical impedance tomography with multiplicative regularization. Inverse Problems and Imaging, 2019, 13 (6) : 1139-1159. doi: 10.3934/ipi.2019051 |
[12] |
Bastian Gebauer. Localized potentials in electrical impedance tomography. Inverse Problems and Imaging, 2008, 2 (2) : 251-269. doi: 10.3934/ipi.2008.2.251 |
[13] |
Sarah J. Hamilton, David Isaacson, Ville Kolehmainen, Peter A. Muller, Jussi Toivanen, Patrick F. Bray. 3D Electrical Impedance Tomography reconstructions from simulated electrode data using direct inversion $ \mathbf{t}^{\rm{{\textbf{exp}}}} $ and Calderón methods. Inverse Problems and Imaging, 2021, 15 (5) : 1135-1169. doi: 10.3934/ipi.2021032 |
[14] |
Kari Astala, Jennifer L. Mueller, Lassi Päivärinta, Allan Perämäki, Samuli Siltanen. Direct electrical impedance tomography for nonsmooth conductivities. Inverse Problems and Imaging, 2011, 5 (3) : 531-549. doi: 10.3934/ipi.2011.5.531 |
[15] |
Helmut Harbrecht, Thorsten Hohage. A Newton method for reconstructing non star-shaped domains in electrical impedance tomography. Inverse Problems and Imaging, 2009, 3 (2) : 353-371. doi: 10.3934/ipi.2009.3.353 |
[16] |
Sarah Jane Hamilton, Andreas Hauptmann, Samuli Siltanen. A data-driven edge-preserving D-bar method for electrical impedance tomography. Inverse Problems and Imaging, 2014, 8 (4) : 1053-1072. doi: 10.3934/ipi.2014.8.1053 |
[17] |
Daniela Calvetti, Paul J. Hadwin, Janne M. J. Huttunen, David Isaacson, Jari P. Kaipio, Debra McGivney, Erkki Somersalo, Joseph Volzer. Artificial boundary conditions and domain truncation in electrical impedance tomography. Part I: Theory and preliminary results. Inverse Problems and Imaging, 2015, 9 (3) : 749-766. doi: 10.3934/ipi.2015.9.749 |
[18] |
Dong liu, Ville Kolehmainen, Samuli Siltanen, Anne-maria Laukkanen, Aku Seppänen. Estimation of conductivity changes in a region of interest with electrical impedance tomography. Inverse Problems and Imaging, 2015, 9 (1) : 211-229. doi: 10.3934/ipi.2015.9.211 |
[19] |
Liliana Borcea, Fernando Guevara Vasquez, Alexander V. Mamonov. Study of noise effects in electrical impedance tomography with resistor networks. Inverse Problems and Imaging, 2013, 7 (2) : 417-443. doi: 10.3934/ipi.2013.7.417 |
[20] |
Nicolay M. Tanushev, Luminita Vese. A piecewise-constant binary model for electrical impedance tomography. Inverse Problems and Imaging, 2007, 1 (2) : 423-435. doi: 10.3934/ipi.2007.1.423 |
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