An analysis of electrical impedance tomography with applications to Tikhonov regularization

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 con- ductivity parameter in Lp-norms are proved. These analytical results are applied to several popular regularization formulations, which incorporate ap rioriinformation of smoothness/sparsity on the inho- mogeneity 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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