An analysis of electrical impedance tomography with applications to Tikhonov regularization

Bangti Jin, Peter Maass

Research output: Contribution to journalArticlepeer-review

47 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

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors would like to thank two anonymous referees for their constructive comments which have led to an improved presentation of the manuscript. The work of Bangti Jin was substantially supported by the Alexander von Humboldt foundation through a postdoctoral researcher fellowship and is partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST), and that of Peter Maass by the German Science Foundation through grant MA 1657/18-1.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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