An analysis of electrical impedance tomography with applications to Tikhonov regularization
KAUST Grant NumberKUS-C1-016-04
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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.
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.
SponsorsThe 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.