Resolution-Controlled Conductivity Discretization in Electrical Impedance Tomography

This work contributes to the numerical solution of the inverse problem of determining an isotropic conductivity from boundary measurements, known as electrical impedance tomography. To this end, we first investigate the imaging resolution of the complete electrode model in a circular geometry using analytic solutions of the forward problem and conformal maps. Based on this information we propose a novel discretization of the conductivity space which explicitly depends on the electrode sizes and locations. Roughly speaking, the resulting conductivity meshes comply with the maximal resolution provided by discrete data with a known noise level. We heuristically extend this approach to domains of arbitrary shape and present its performance under a Newton-type inversion algorithm.