A regularized weighted least gradient problem for conductivity imaging

TL;DR

This paper introduces a regularization approach for electrical conductivity imaging using interior current density magnitude, addressing nonuniqueness issues and demonstrating computational effectiveness through numerical experiments.

Contribution

It presents a novel regularization method based on a weighted least gradient problem for conductivity imaging from interior current data.

Findings

The method effectively recovers approximate conductivity.

Numerical experiments demonstrate computational efficiency.

Addresses nonuniqueness in conductivity reconstruction.

Abstract

We propose and study a regularization method for recovering an approximate electrical conductivity solely from the magnitude of one interior current density field. Without some minimal knowledge of the boundary voltage potential, the problem has been recently shown to have nonunique solutions, thus recovering the exact conductivity is impossible. The method is based on solving a weighted least gradient problem in the subspace of functions of bounded variations with square integrable traces. The computational effectiveness of this method is demonstrated in numerical experiments.