An analytical solution for the inverse conductivity problem

Abstract

We present an image reconstruction algorithm for the Inverse conductivity Problem based on reformulating the problem in terms of integral equations. By using a priori information we aic able to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind and then by solving a first order partial differential equation for the conductivity cr(x). Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.