Topological Bayesian inversion for the inverse conductivity problem

Abstract

The employment of topological derivative concept is considered to propose a new opti- mization algorithm for the inverse conductivity problem. Since this inverse problem is nonlinear and ill-posed it is necessary to incorporate a prior knowledge about the unknown conductivity. In particular, we apply the Bayes theorem to add the assumption that we have just one small ball- shaped inclusion, which must be at a certain distance from the boundary of the domain. As the main emphasis of this paper is to investigate numerically the proposed approach, we shall present some numerical results to show that accurate results, even for noisy data, can be obtained with small computational cost.