Numerical implementation of an integral equation method for the inverse conductivity problem

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Abstract
We seek to recover the interior electrical conductivity of an inhomogeneous object by linearizing the inverse conductivity problem as suggested by Calderon. First, we reduce the Dirichlet-to-Neumann data to the data of the problem in the whole with point sources and suggest a linearization of this new, simpler linear inverse problem. Then, we study and solve numerically the linear ill-posed problem by using regularization. The FORTRAN programs that numerically implement the algorithm show that the method is reasonably accurate for reconstruction of conductivity distribution and reproduces the location and shapes of conducting objects well.