Reconstruction of less regular conductivities in the plane

Details Reconstruction of less regular conductivities in the plane Reconstruction of less regular conductivities in the plane

2001-10-26

arxiv.org/abs/math/0110298v1

Mathematics

Functional Analysis

Scientific paper

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.

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