Approximation of the inverse electrical impedance tomography problem by an inverse transmission problem

The inverse problem in electrical impedance tomography (EIT) is severely ill-posed. Therefore, it is desirable to include any available a priori information in a numerical algorithm for its solution. If the conductivity inside the object is known to be piecewise constant this information can be directly incorporated in the algorithm by using boundary integral methods for the computation of the forward map. In this paper we will describe an implementation of this idea and compare the results with standard methods using both synthetic and measured data from the clinical applications of EIT.