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Determining nonsmooth first order terms from partial boundary measurements
Approximation errors and truncation of computational domains with application to geophysical tomography
1. | Department of Physics, University of Kuopio, P.O. Box 1627, FIN-70211 Kuopio, Finland, Finland, Finland, Finland |
2. | Lawrence Berkeley National Laboratory (LBNL), University of California, Berkeley, CA 94720, United States |
[1] |
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 |
[2] |
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 |
[3] |
Janne M.J. Huttunen, J. P. Kaipio. Approximation errors in nonstationary inverse problems. Inverse Problems and Imaging, 2007, 1 (1) : 77-93. doi: 10.3934/ipi.2007.1.77 |
[4] |
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 |
[5] |
Melody Alsaker, Benjamin Bladow, Scott E. Campbell, Emma M. Kar. Automated filtering in the nonlinear Fourier domain of systematic artifacts in 2D electrical impedance tomography. Inverse Problems and Imaging, 2022, 16 (3) : 647-671. doi: 10.3934/ipi.2021066 |
[6] |
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 |
[7] |
Daijun Jiang, Hui Feng, Jun Zou. Overlapping domain decomposition methods for linear inverse problems. Inverse Problems and Imaging, 2015, 9 (1) : 163-188. doi: 10.3934/ipi.2015.9.163 |
[8] |
Frank Hettlich. The domain derivative for semilinear elliptic inverse obstacle problems. Inverse Problems and Imaging, 2022, 16 (4) : 691-702. doi: 10.3934/ipi.2021071 |
[9] |
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 |
[10] |
Bastian Gebauer. Localized potentials in electrical impedance tomography. Inverse Problems and Imaging, 2008, 2 (2) : 251-269. doi: 10.3934/ipi.2008.2.251 |
[11] |
Martin Hanke, William Rundell. On rational approximation methods for inverse source problems. Inverse Problems and Imaging, 2011, 5 (1) : 185-202. doi: 10.3934/ipi.2011.5.185 |
[12] |
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 |
[13] |
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 |
[14] |
Chuang Zheng. Inverse problems for the fourth order Schrödinger equation on a finite domain. Mathematical Control and Related Fields, 2015, 5 (1) : 177-189. doi: 10.3934/mcrf.2015.5.177 |
[15] |
Shui-Nee Chow, Ke Yin, Hao-Min Zhou, Ali Behrooz. Solving inverse source problems by the Orthogonal Solution and Kernel Correction Algorithm (OSKCA) with applications in fluorescence tomography. Inverse Problems and Imaging, 2014, 8 (1) : 79-102. doi: 10.3934/ipi.2014.8.79 |
[16] |
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 |
[17] |
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 |
[18] |
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 |
[19] |
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 |
[20] |
Nuutti Hyvönen, Lassi Päivärinta, Janne P. Tamminen. Enhancing D-bar reconstructions for electrical impedance tomography with conformal maps. Inverse Problems and Imaging, 2018, 12 (2) : 373-400. doi: 10.3934/ipi.2018017 |
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