An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

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 L p-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. © EDP Sciences, SMAI, 2012.
Original languageEnglish (US)
Pages (from-to)1027-1048
Number of pages22
JournalESAIM: Control, Optimisation and Calculus of Variations
Volume18
Issue number4
DOIs
StatePublished - Jan 16 2012
Externally publishedYes

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