A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data

TL;DR

This paper introduces a globally convergent numerical method for reconstructing dielectric constants in 3D from single-measurement multi-frequency data, avoiding local minima issues common in traditional optimization approaches.

Contribution

The paper develops and proves a globally convergent algorithm for a 3D coefficient inverse problem using minimal measurement data, with no prior knowledge needed.

Findings

Algorithm accurately reconstructs dielectric constants from simulated data.

Method successfully applied to experimental data.

Provides reliable reconstructions without initial guess dependence.

Abstract

The goal of this paper is to reconstruct spatially distributed dielectric constants from complex-valued scattered wave field by solving a 3D coefficient inverse problem for the Helmholtz equation at multi-frequencies. The data are generated by only a single direction of the incident plane wave. To solve this inverse problem, a globally convergent algorithm is analytically developed. We prove that this algorithm provides a good approximation for the exact coefficient without any \textit{a priori} knowledge of any point in a small neighborhood of that coefficient. This is the main advantage of our method, compared with classical approaches using optimization schemes. Numerical results are presented for both computationally simulated data and experimental data. Potential applications of this problem are in detection and identification of explosive-like targets.