A globally convergent method for a 3-D inverse medium problem for the generalized Helmholtz equation

TL;DR

This paper introduces a new globally convergent numerical method for reconstructing dielectric constants in a 3-D inverse medium problem related to the Helmholtz equation, with applications in explosive target detection.

Contribution

The paper proposes a novel numerical method that guarantees global convergence for a 3-D inverse medium problem without requiring initial neighborhood knowledge.

Findings

Method achieves global convergence in numerical experiments.

Effective in reconstructing dielectric properties from backscattering data.

Applicable to detection of explosive-like targets.

Abstract

A 3-D inverse medium problem in the frequency domain is considered. Another name for this problem is Coefficient Inverse Problem. The goal is to reconstruct spatially distributed dielectric constants from scattering data. Potential applications are in detection and identification of explosive-like targets. A single incident plane wave and multiple frequencies are used. A new numerical method is proposed. A theorem is proved, which claims that a small neigborhood of the exact solution of that problem is reached by this method without any advanced knowledge of that neighborhood. We call this property of that numerical method "global convergence". Results of numerical experiments for the case of the backscattering data are presented.