Multiple coefficient identification in electrical impedance tomography with energy functional method
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In this paper we investigate the problem of simultaneously identifying the conductivity and the reaction in electrical impedance tomography with available measurement data on an accessible part of the boundary. We propose an energy functional method and the total variational regularization combining with the quadratic stabilizing term to tackle the identification problem. We show the stability of the proposed regularization method and the convergence of the finite element regularized solutions to the identification in the Lebesgue spaces and in the sense of the Bregman distance with respect to the total variation semi-norm. To illustrate the theoretical results, a numerical case study is presented which supports our analytical findings.
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