An analysis of electrical impedance tomography with applications to Tikhonov regularization

Handle URI:
http://hdl.handle.net/10754/597509
Title:
An analysis of electrical impedance tomography with applications to Tikhonov regularization
Authors:
Jin, Bangti; Maass, Peter
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.
Citation:
Jin B, Maass P (2012) An analysis of electrical impedance tomography with applications to Tikhonov regularization. ESAIM: Control, Optimisation and Calculus of Variations 18: 1027–1048. Available: http://dx.doi.org/10.1051/cocv/2011193.
Publisher:
EDP Sciences
Journal:
ESAIM: Control, Optimisation and Calculus of Variations
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
16-Jan-2012
DOI:
10.1051/cocv/2011193
Type:
Article
ISSN:
1292-8119; 1262-3377
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorJin, Bangtien
dc.contributor.authorMaass, Peteren
dc.date.accessioned2016-02-25T12:41:08Zen
dc.date.available2016-02-25T12:41:08Zen
dc.date.issued2012-01-16en
dc.identifier.citationJin B, Maass P (2012) An analysis of electrical impedance tomography with applications to Tikhonov regularization. ESAIM: Control, Optimisation and Calculus of Variations 18: 1027–1048. Available: http://dx.doi.org/10.1051/cocv/2011193.en
dc.identifier.issn1292-8119en
dc.identifier.issn1262-3377en
dc.identifier.doi10.1051/cocv/2011193en
dc.identifier.urihttp://hdl.handle.net/10754/597509en
dc.description.abstractThis 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.en
dc.description.sponsorshipThe 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.en
dc.publisherEDP Sciencesen
dc.subjectConvergence rateen
dc.subjectElectrical impedance tomographyen
dc.subjectTikhonov regularizationen
dc.titleAn analysis of electrical impedance tomography with applications to Tikhonov regularizationen
dc.typeArticleen
dc.identifier.journalESAIM: Control, Optimisation and Calculus of Variationsen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
dc.contributor.institutionUniversitat Bremen, Bremen, Germanyen
kaust.grant.numberKUS-C1-016-04en
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