A filtering approach to the two-dimensional volume conductor forward and inverse problems

Abstract

Summary form only given. The volume conductor inverse problem is the problem of reconstructing a two-dimensional distributed voltage source from measurements of the electric field it produces at the surface of an intervening medium. The intervening medium may be homogeneous or horizontally layered, with differing conductivities in each layer. The problem is assumed to be quasistatic (a 'snapshot' in time); this is reasonable for the impedances encountered in biological tissues. The distributed source potential and the surface data are regarded as two-dimensional signals, and they are shown to be related by a linear two-dimensional filter. Implementation of the medium filter requires signal processing filtering techniques. This inverse problem is ill-conditioned for high-frequency signals and for large distances between source and measurements. The use of data-conditioning filters regularizes the inverse problem, with only minor effect on the reconstructed potential distribution. For typical signals under realistic signal-to-noise ratios, excellent numerical results have been obtained. In particular, a numerically stable recursive algorithm for computing the coefficients of the two-dimensional medium filter has been developed.<>