Reconstruction of less regular conductivities in the plane

Abstract

We study the inverse conductivity problem of how to reconstruct an isotropic electrical conductivity distribution $\gamma$ in an object from static electrical measurements on the boundary of the object. We give an exact reconstruction algorithm for the conductivity \gamma\in C^{1+\epsilon}(\ol \Om) in the plane domain $\Omega$ from the associated Dirichlet to Neumann map on \partial \Om. Hence we improve earlier reconstruction results. The method used relies on a well-known reduction to a first order system, for which the \ol\partial-method of inverse scattering theory can be applied