Numerical implementation of the factorization method within the complete electrode model of electrical impedance tomography

Abstract

In electrical impedance tomography, one tries to recover the spatial conductivitydistribution inside a body from boundary measurements of current and voltage.In many practically important situations, the object has known backgroundconductivity but it is contaminated by inhomogeneities.The factorization method of Andreas Kirsch provides a tool for locatingsuch inclusions. In earlier work, it has been shown, both theoretically andnumerically, that the inhomogeneities can be characterized by the factorization techniqueif the input current can be controlled and the potential can be measured everywhere onthe object boundary. However, in real-world electrode applications, one can onlycontrol the net currents through certain surface patches and measure thecorresponding potentials on the electrodes. In this work,the factorization method is translated to the framework of the complete electrode modelof electrical impedance tomography and its functionality is demonstrated through two-dimensionalnumerical experiments. Special attention is paid to the efficient implementation of thealgorithm in polygonal domains.