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.
@article{arxiv.1602.09092,
title = {A globally convergent numerical method for a 1-d inverse medium problem with experimental data},
author = {Michael V. Klibanov and Loc H. Nguyen and Anders Sullivan and Lam Nguyen},
journal= {arXiv preprint arXiv:1602.09092},
year = {2016}
}