期刊
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
卷 18, 期 4, 页码 1027-1048出版社
EDP SCIENCES S A
DOI: 10.1051/cocv/2011193
关键词
Electrical impedance tomography; Tikhonov regularization; convergence rate
资金
- Alexander von Humboldt foundation
- King Abdullah University of Science and Technology (KAUST) [KUS-C1-016-04]
- German Science Foundation [MA 1657/18-1]
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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