Incorporating knowledge on the measurement noise in electrical impedance tomography

The present article is concerned with the identification of an obstacle or void of different conductivity which is included in a two-dimensional domain by measurements of voltage and currents at the boundary. In general, the voltage distribution is prescribed and hence deterministic. Whereas, the current distribution is measured and contains measurement errors. We assume that some information is given on these measurement errors which can be described by means of a random field. We exploit this extra knowledge by minimizing a linear combination of the expectation and the variance of the Kohn-Vogelius functional. It is shown how these ideas can be realized in numerical computations. By numerical results, the applicability and feasibility of our approach is demonstrated.