An analysis of electrical impedance tomography with applications to Tikhonov regularization

¹ Department of Mathematics and Institute for Applied Mathematics and Computational Sciences, Texas A&M University, College Station, 77843-3368 TX, USA
btjin@math.tamu.edu
² Center for Industrial Mathematics, University of Bremen, 28334 Bremen, Germany
pmaass@math.uni-bremen.de

Received: 23 December 2010
Revised: 1 June 2011

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.