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

Michael V. Klibanov; Loc H. Nguyen; Anders Sullivan; Lam Nguyen

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arXiv · 1602.09092

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

Michael V. Klibanov·Loc H. Nguyen·Anders Sullivan·Lam Nguyen

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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.

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Michael V. Klibanov, Loc H. Nguyen, Anders Sullivan, Lam Nguyen. 2016-02-29. A globally convergent numerical method for a 1-d inverse medium problem with experimental data. https://arxiv.org/abs/1602.09092

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