An integral equation method for the inverse conductivity problem

Details An integral equation method for the inverse conductivity problem An integral equation method for the inverse conductivity problem

2004-03-11

arxiv.org/abs/math-ph/0403015v2

Phys. Lett. A 325 (2004) 253-267

Physics

Mathematical Physics

15 pages, 8 figures

Scientific paper

10.1016/j.physleta.2004.03.060

We present an image reconstruction algorithm for the Inverse Conductivity Problem based on reformulating the problem in terms of integral equations. We use as data the values of injected electric currents and of the corresponding induced boundary potentials, as well as the boundary values of the electrical conductivity. We have used a priori information to find a regularized conductivity distribution by first solving a Fredholm integral equation of the second kind for the Laplacian of the potential, and then by solving a first order partial differential equation for the regularized conductivity itself. Many of the calculations involved in the method can be achieved analytically using the eigenfunctions of an integral operator defined in the paper.

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