Numerical method for determining the inhomogeneity boundary in the electrical impedance tomography problem in the case of piecewise constant conductivity
Matematičeskoe modelirovanie, Tome 32 (2020) no. 11, pp. 59-69.

Voir la notice de l'article provenant de la source Math-Net.Ru

A two-dimentional electrical impedance tomography problem in case of piecewise constant electrical conductivity taking two known values is considered. The task is to determine the unknown boundary separating regions with different conductivity values. Initial data represents several pairs of current and voltage distributions on the outer boundary of an object. A numerical method for determining the unknown boundary is proposed, numerical results are presented.
Keywords: electrical impedance tomography, piecewise constant conductivity, unknown boundary, numerical method.
@article{MM_2020_32_11_a4,
     author = {S. V. Gavrilov},
     title = {Numerical method for determining the inhomogeneity boundary in the electrical impedance tomography problem in the case of piecewise constant conductivity},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {59--69},
     publisher = {mathdoc},
     volume = {32},
     number = {11},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2020_32_11_a4/}
}
TY  - JOUR
AU  - S. V. Gavrilov
TI  - Numerical method for determining the inhomogeneity boundary in the electrical impedance tomography problem in the case of piecewise constant conductivity
JO  - Matematičeskoe modelirovanie
PY  - 2020
SP  - 59
EP  - 69
VL  - 32
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2020_32_11_a4/
LA  - ru
ID  - MM_2020_32_11_a4
ER  - 
%0 Journal Article
%A S. V. Gavrilov
%T Numerical method for determining the inhomogeneity boundary in the electrical impedance tomography problem in the case of piecewise constant conductivity
%J Matematičeskoe modelirovanie
%D 2020
%P 59-69
%V 32
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2020_32_11_a4/
%G ru
%F MM_2020_32_11_a4
S. V. Gavrilov. Numerical method for determining the inhomogeneity boundary in the electrical impedance tomography problem in the case of piecewise constant conductivity. Matematičeskoe modelirovanie, Tome 32 (2020) no. 11, pp. 59-69. http://geodesic.mathdoc.fr/item/MM_2020_32_11_a4/

[1] D. S. Holder, Electrical impedance tomography: methods, history and applications, Series in Medical Physics and Biomedical Engineering, 1st Ed., CRC Press, UK, 2004, 456 pp. | DOI

[2] K. Karhunen, A. Seppanen, A. Lehikoinen, P.J.M. Monteiro, J.P. Kaipio, “Electrical Resistance Tomography imaging of concrete”, Cement Concrete Res., 40 (2010), 137–145 | DOI

[3] I. Frerichs, M.B.P. Amato, A.H. van Kaam et al., “Chest electrical impedance tomography examination, data analysis, terminology, clinical use and recommendations: consensus statement of the Translational EIT development study group”, Thorax, 72 (2017), 83–93 | DOI

[4] A. P. Calderon, “On an inverse boundary value problem”, Seminar on Num. Anal. and its applications to Contin. Phys., Soc. Brasileira de Matematica, Rio de Janeiro, 1980, 65–73 | MR

[5] B. Barceo, E. Fabes, J. K. Seo, “The inverse conductivity problem with one measurement: uniqueness for convex polyhedra”, Proc. Amer. Math. Soc., 122:1 (1994), 183–189 | DOI | MR

[6] G. Alessandrini, V. Isakov, “Analiticity and uniqueness for the inverse conductivity problem”, Rend. Ist. Mat. Univ. Trieste, 28 (1996), 351–369 | MR | Zbl

[7] M. Ikehata, “On reconstruction in the inverse conductivity problem with one measurement”, Inverse Problems, 16:3 (2000), 785–793 | DOI | MR | Zbl

[8] H. Kang, J. K. Seo, D. Sheen, “Numerical identification of discontinuous conductivity coefficients”, Inverse Problems, 13 (1997), 113–123 | DOI | MR | Zbl

[9] O. Kwon, J. K. Seo, J. R. Yoon, “A real-time algorithm for the location search of discontinu-ous conductivities with one measurement”, Comm. Pure Appl. Math., 55:1 (2002), 1–29 | DOI | MR | Zbl

[10] M. Dambrine, D. Kateb, “Conformal mapping and inverse conductivity problem with one measurement”, ESAIM: Control, Optimisation and Calculus of Variations, 13:1 (2007), 163–177 | DOI | MR | Zbl

[11] H. Eckel, R. Kress, “Nonlinear integral equations for the inverse electrical impedance problem”, Inverse Problems, 23 (2007), 475–491 | DOI | MR | Zbl

[12] S. V. Gavrilov, A. M. Denisov, “Numerical method for determining the inhomogeneity boundary in the Dirichlet problem for Laplace's equation in a piecewise homogeneous medium”, Computational Math. and Mathematical Phys., 50:8 (2010), 1391–1398 | DOI | MR | Zbl

[13] S. V. Gavrilov, “Numerical method for solving an inverse problem for Laplace's equation in a domain with an unknown inner boundary”, CM MP, 59:1 (2019), 59–65 | MR | Zbl

[14] S. V. Gavrilov, A. M. Denisov, “A numerical method for solving a three-dimentional electrical impedance tomography problem in the case of the data given on part of the boundary”, Mathematical Models and Computer Simulations, 8:4 (2016), 369–381 | DOI | MR

[15] F. P. Vasil'ev, M. M. Potapov, B. A. Budak, L. A. Artem'eva, Optimization Methods, Urait, M., 2016, 375 pp.

[16] V. Maz'ya, G. Schmidt, Approximate approximations, Mathematical Surveys and Monographs, Amer. Math. Soc., 2007, 349 pp. | DOI | MR | Zbl

[17] V. B. Andreev, Numerical Methods, Textbook, MAKS Press, M., 2013, 336 pp.