A globally convergent numerical method for a 1-d inverse medium problem with experimental data

TL;DR

This paper introduces a globally convergent algorithm using the Quasi-Reversibility Method for reconstructing the dielectric constant in a 1-D inverse medium problem, validated on simulated and experimental data.

Contribution

It presents a novel globally convergent reconstruction algorithm that does not require prior solution neighborhood knowledge, with proven convergence via Carleman estimates.

Findings

Successful reconstruction on simulated data

Effective application to experimental data

Proven convergence of the method

Abstract

In this paper, a reconstruction method for the spatially distributed dielectric constant of a medium from the back scattering wave field in the frequency domain is considered. Our approach is to propose a globally convergent algorithm, which does not require any knowledge of a small neighborhood of the solution of the inverse problem in advance. The Quasi-Reversibility Method (QRM) is used in the algorithm. The convergence of the QRM is proved via a Carleman estimate. The method is tested on both computationally simulated and experimental data.