Abstract
We consider the two-dimensional inverse electrical impedance problem in the case of piecewise constant conductivities. Our approach is based on a system of nonlinear integral equations from which the unknown shapes of the subdomains with constant conductivity and the unknown conductivities are obtained iteratively via linearization. Our approach extends a method that has been suggested by Kress and Rundell (2005 Inverse Problems 21 1207–23) for the case of a perfectly conducting inclusion. For the choice of the regularization parameters occurring in the algorithm we suggest an evolutionary algorithm and the initial guess for the iterations is obtained through employing the factorization method. We describe the method in detail and illustrate its feasibility by numerical examples.
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