This paper analyzes the continuum model/complete electrode model in the electrical impedance tomography inverse problem of determining the conductivity parameter from boundary measurements. The continuity and differentiability of the forward operator with respect to the conductivity parameter in Lp-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate a priori information of smoothness/sparsity on the inhomogeneity through Tikhonov regularization, for both linearized and nonlinear models. Some important properties, e.g., existence, stability, consistency and convergence rates, are established. This provides some theoretical justifications of their practical usage.
Mots-clés : electrical impedance tomography, Tikhonov regularization, convergence rate
@article{COCV_2012__18_4_1027_0,
author = {Jin, Bangti and Maass, Peter},
title = {An analysis of electrical impedance tomography with applications to {Tikhonov} regularization},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {1027--1048},
publisher = {EDP-Sciences},
volume = {18},
number = {4},
year = {2012},
doi = {10.1051/cocv/2011193},
mrnumber = {3019471},
zbl = {1259.49056},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2011193/}
}
TY - JOUR AU - Jin, Bangti AU - Maass, Peter TI - An analysis of electrical impedance tomography with applications to Tikhonov regularization JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2012 SP - 1027 EP - 1048 VL - 18 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2011193/ DO - 10.1051/cocv/2011193 LA - en ID - COCV_2012__18_4_1027_0 ER -
%0 Journal Article %A Jin, Bangti %A Maass, Peter %T An analysis of electrical impedance tomography with applications to Tikhonov regularization %J ESAIM: Control, Optimisation and Calculus of Variations %D 2012 %P 1027-1048 %V 18 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2011193/ %R 10.1051/cocv/2011193 %G en %F COCV_2012__18_4_1027_0
Jin, Bangti; Maass, Peter. An analysis of electrical impedance tomography with applications to Tikhonov regularization. ESAIM: Control, Optimisation and Calculus of Variations, Tome 18 (2012) no. 4, pp. 1027-1048. doi : 10.1051/cocv/2011193. http://archive.numdam.org/articles/10.1051/cocv/2011193/
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