Reconstruction of small and extended regions in EIT with a Robin transmission condition

TL;DR

This paper develops and compares two methods, MUSIC-type and factorization, for reconstructing small and extended corroded regions in electrical impedance tomography using a Robin boundary condition.

Contribution

It introduces a novel application of MUSIC and factorization methods for EIT with Robin conditions to recover corrosion regions of different sizes.

Findings

MUSIC-type algorithm effectively recovers small regions via asymptotic expansion.

Factorization method successfully reconstructs extended regions.

Numerical examples demonstrate the methods' effectiveness in 2D simulations.

Abstract

We consider an inverse shape problem coming from electrical impedance tomography with a Robin transmission condition. In general, a boundary condition of Robin type models corrosion. In this paper, we study two methods for recovering an interior corroded region from electrostatic data. We consider the case where we have small volume and extended regions. For the case where the region has small volume, we will derive an asymptotic expansion of the current gap operator and prove that a MUSIC-type algorithm can be used to recover the region. In the case where one has an extended region, we will show that the regularized factorization method can be used to recover said region. Numerical examples will be presented for both cases in two dimensions in the unit circle.