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.

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.

DOI : https://doi.org/10.1051/cocv/2011193
Classification : 49N45,  65N21
Mots clés : electrical impedance tomography, Tikhonov regularization, convergence rate
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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://www.numdam.org/articles/10.1051/cocv/2011193/

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