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An integral equation method for the inverse conductivity problem
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.Comment: 15 pages, 8 figure