On reconstruction of complex-valued once differentiable conductivities

TL;DR

This paper extends the $ar{ ext{d}}$-method to handle exceptional points, enabling the reconstruction of complex-valued, once differentiable conductivities in inverse impedance tomography with minimal smoothness assumptions.

Contribution

It introduces a generalized $ar{ ext{d}}$-method for inverse scattering that works under weak smoothness conditions on potentials.

Findings

Effective reconstruction of complex conductivities demonstrated

Method handles exceptional points in inverse scattering

Applicable to weakly smooth potentials

Abstract

The classical $\overline \partial$-method has been generalized recently [lnv], [lnv2] to be used in the presence of exceptional points. We apply this generalization to solve Dirac inverse scattering problem with weak assumptions on smoothness of potentials. As a consequence, this provides an effective method of reconstruction of complex-valued one time differentiable conductivities in the inverse impedance tomography problem.