Qualitative reconstruction methods for imaging interior Robin interfaces in EIT from Robin-to-Dirichlet data

TL;DR

This paper introduces non-iterative qualitative methods using the Linear Sampling Method and Regularized Factorization Method to reconstruct interior Robin interfaces in electrical impedance tomography, utilizing Robin-to-Dirichlet data.

Contribution

It develops new analytical characterizations and numerical strategies for qualitative interior reconstruction in EIT with Robin boundary conditions, expanding existing methods.

Findings

Methods reliably reconstruct interior regions in experiments.

New analytical characterizations enable interface identification.

Regularization improves numerical stability and accuracy.

Abstract

We consider an inverse shape problem arising in electrical impedance tomography (EIT) for nondestructive testing, in which interior defects are modeled through Robin transmission conditions. Unlike classical formulations, we impose Robin boundary conditions on both the exterior measurement surface and the interior interface, and use the Robin-to-Dirichlet (RtD) map as the available data. Within this setting, we develop qualitative (non-iterative) reconstruction methods based on the Linear Sampling Method (LSM) and the Regularized Factorization Method (RFM), and derive new analytical characterizations that enable these methods to identify interior regions. We further propose a numerical implementation that incorporates regularization strategies and demonstrate, through experiments, that the methods reliably reconstruct interior regions of interest.