Volume 18, Number 4, October-December 2012
|Page(s)||1027 - 1048|
|Published online||16 January 2012|
An analysis of electrical impedance tomography with applications to Tikhonov regularization
Department of Mathematics and Institute for Applied Mathematics
and Computational Sciences, Texas A&M University, College Station, 77843-3368
2 Center for Industrial Mathematics, University of Bremen, 28334 Bremen, Germany
Revised: 1 June 2011
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.
Mathematics Subject Classification: 49N45 / 65N21
Key words: Electrical impedance tomography / Tikhonov regularization / convergence rate
© EDP Sciences, SMAI, 2012
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