Reconstruction of less regular conductivities in the plane

TL;DR

This paper presents an exact reconstruction algorithm for isotropic electrical conductivities in a plane domain from boundary measurements, improving previous results by leveraging inverse scattering theory and a reduction to a first order system.

Contribution

The paper introduces a novel exact reconstruction method for less regular conductivities in the plane, extending prior techniques with a new application of the $ar ext{d}$-method.

Findings

Provides an explicit reconstruction algorithm for $C^{1+ ext{epsilon}}$ conductivities.

Improves upon earlier reconstruction results in the inverse conductivity problem.

Utilizes inverse scattering theory and a reduction to a first order system.

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.