A direct reconstruction algorithm for the anisotropic inverse conductivity problem based on Calder\'on's method in the plane

TL;DR

This paper introduces a Calderón-based direct reconstruction algorithm for anisotropic conductivities in 2D, assuming known tensor entries, and demonstrates its effectiveness on radially symmetric cases.

Contribution

It extends Calderón's linearization method to anisotropic conductivities by assuming known tensor entries, enabling scalar field reconstruction in 2D.

Findings

Effective reconstruction of anisotropic conductivities demonstrated

Method handles discontinuous radially symmetric conductivities

Overcomes non-uniqueness by assuming known tensor entries

Abstract

A direct reconstruction algorithm based on Calder\'on's linearization method for the reconstruction of isotropic conductivities is proposed for anisotropic conductivities in two-dimensions. To overcome the non-uniqueness of the anisotropic inverse conductivity problem, the entries of the unperturbed anisotropic tensors are assumed known \emph{a priori}, and it remains to reconstruct the multiplicative scalar field. The quasi-conformal map in the plane facilitates the Calder\'on-based approach for anisotropic conductivities. The method is demonstrated on discontinuous radially symmetric conductivities of high and low contrast.