Journal
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
Volume 18, Issue 4, Pages 1027-1048Publisher
EDP SCIENCES S A
DOI: 10.1051/cocv/2011193
Keywords
Electrical impedance tomography; Tikhonov regularization; convergence rate
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Funding
- Alexander von Humboldt foundation
- King Abdullah University of Science and Technology (KAUST) [KUS-C1-016-04]
- German Science Foundation [MA 1657/18-1]
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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.
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