Enhancing residual-based techniques with shape reconstruction features in Electrical Impedance Tomography

TL;DR

This paper introduces a new regularized residual minimization method for electrical impedance tomography that guarantees global convergence and produces artifact-free shape reconstructions even under high noise levels.

Contribution

It proposes a novel approach combining residual minimization with a monotonicity-based regularizer, providing the first rigorous convergence analysis for this class of algorithms.

Findings

Method achieves stable, high-quality shape reconstructions with noise.

Guarantees global convergence despite noise.

Reduces ringing artifacts in reconstructions.

Abstract

In electrical impedance tomography, algorithms based on minimizing a linearized residual functional have been widely used due to their flexibility and good performance in practice. However, no rigorous convergence results have been available in the literature yet, and reconstructions tend to contain ringing artifacts. In this work, we shall minimize the linearized residual functional under a linear constraint defined by a monotonicity test, which plays a role of a special regularizer. Global convergence is then established to guarantee that this method is stable under the effects of noise. Moreover, numerical results show that this method yields good shape reconstructions under high levels of noise without appearance of artifacts.