ANOMALOUS THRESHOLDS AND EDGE SINGULARITIES IN ELECTRICAL-IMPEDANCE TOMOGRAPHY

Studies of models of current flow behaviour in electrical impedance to mography (EIT) have shown that the current density distribution varies extremely rapidly near the edge of the electrodes used in the techniq ue. This behaviour imposes severe restrictions on the numerical techni ques used in image reconstruction algorithms, In this paper we have co nsidered a simple two dimensional case and we have shown how the theor y of end point/pinch singularities which was developed for studying th e anomalous thresholds encountered in elementary particle physics can be used to give a complete description of the analytic structure of th e current density neat to the edge of the electrodes. As a byproduct o f this study it was possible to give a complete description of the Rie mann sheet manifold of the eigenfunctions of the logarithmic kernel. T hese methods can be readily extended to other weakly singular kernels. (C) 1996 American Institute of Physics.