Identifying conductivity in electrical impedance tomography with total variation regularization

TL;DR

This paper introduces a variational method with total variation regularization for identifying conductivity in electrical impedance tomography, demonstrating stability, convergence, and effective numerical solutions through experiments.

Contribution

It proposes a novel variational approach with total variation regularization for conductivity identification in EIT, including stability proof and a new numerical algorithm.

Findings

The method is stable and convergent.

Numerical experiments validate the theoretical results.

The projected Armijo algorithm effectively solves the discretized problem.

Abstract

In this paper we investigate the problem of identifying conductivity in electrical impedance tomography from one boundary measurement. A variational method with total variation regularization is here proposed to tackle this problem. We discretize the PDE as well as the conductivity with piecewise linear, continuous finite elements. We prove the stability and convergence of this technique. For the numerical solution we propose a projected Armijo algorithm. Finally, a numerical experiment is presented to illustrate our theoretical results.