V. Isakov et A. Sever, NUMERICAL IMPLEMENTATION OF AN INTEGRAL-EQUATION METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM, Inverse problems, 12(6), 1996, pp. 939-951
We seek to recover the interior electrical conductivity of an inhomoge
neous object by linearizing the inverse conductivity problem as sugges
ted by Calderon. First, we reduce the Dirichlet-to-Neumann data to the
data of the problem in the whole R(2) 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 regu
larization. The FORTRAN programs that numerically implement the algori
thm show that the method is reasonably accurate for reconstruction of
conductivity distribution and reproduces the location and shapes of co
nducting objects well.