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An analysis of electrical impedance tomography withapplications to Tikhonov regularization

Published online by Cambridge University Press:  16 January 2012

Bangti Jin  and
Peter Maass
Bangti Jin
Affiliation:
Department of Mathematics and Institute for Applied Mathematics and Computational Sciences, Texas A&M University, College Station, 77843-3368 TX, USA. btjin@math.tamu.edu
Peter Maass
Affiliation:
Center for Industrial Mathematics, University of Bremen, 28334 Bremen, Germany; pmaass@math.uni-bremen.de
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Abstract

This paper analyzes the continuum model/complete electrode model in the electricalimpedance tomography inverse problem of determining the conductivity parameter fromboundary measurements. The continuity and differentiability of the forward operator withrespect to the conductivity parameter inLp-norms are proved. These analytical resultsare applied to several popular regularization formulations, which incorporate apriori information of smoothness/sparsity on the inhomogeneity through Tikhonovregularization, for both linearized and nonlinear models. Some important properties,e.g., existence, stability, consistency andconvergence rates, are established. This provides some theoretical justifications of theirpractical usage.

Keywords

Electrical impedance tomographyTikhonov regularizationconvergence rate
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 18 , Issue 4 , October 2012 , pp. 1027 - 1048
Copyright
© EDP Sciences, SMAI, 2012

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