Reconstruction of less regular conductivities in the plane
Kim Knudsen and Alexandru Tamasan
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 $\gamma\in C^{1+\epsilon}(\overline \Omega)$ in the plane domain $\Omega$ from the associated Dirichlet to Neumann map on $\partial\,\Omega.$ Hence we improve earlier reconstruction results. The method used relies on a well-known reduction to a first order system, for which the $\overline\partial$-method of inverse scattering theory can be applied.