CONVERGENCE OF A RECONSTRUCTION METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM

The inverse conductivity problem is that of reconstructing a spatially varying isotropic conductivity in the interior of some region by means of steady-state measurements taken at the boundary. Reconstruction schemes including least-squares type minimization methods have been widely studied and implemented, but convergence analysis has been largely ignored. This paper establishes the convergence of a well-known least-squares minimization scheme-the Levenberg Marquardt method-on a regularized formulation of the inverse conductivity problem.