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.
Highlights
In this paper we develop a globally convergent numerical method for a 1-d inverse medium problem in the frequency domain
Our interest is in the following inverse problem problem: Problem (Coefficient Inverse Problem (CIP))
We have modeled the process of electromagnetic waves propagation by the 1-d wave-like PDE
Summary
In this paper we develop a globally convergent numerical method for a 1-d inverse medium problem in the frequency domain. The performance of this method is tested on both computationally simulated and experimental data. In terms of working with experimental data, the goal in this paper is not to image locations of targets, since this is impossible via solving a CIP with our data, see subsection 6.2 for details. In the 3-d case the globally convergent method of [1, 2, 28, 29] works with the data generated either by a single location of the source or by a single direction of the incident plane wave.
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