On the numerical solution to an inverse medium problem

TL;DR

This paper introduces a fast, robust sampling indicator function for inverse medium problems, capable of recovering object shape and location from near-field or far-field data without solving ill-posed problems.

Contribution

It proposes a flexible, simple indicator function with resolution and stability analysis, applicable to various measurement regimes, and validated on simulated and experimental data.

Findings

Effective in both near-field and far-field data scenarios

Does not require solving ill-posed inverse problems

Validated with simulated and experimental data

Abstract

This paper is concerned with the inverse medium problem of determining the location and shape of penetrable scattering objects from measurements of the scattered field. We study a sampling indicator function for recovering the scattering object in a fast and robust way. A flexibility of this indicator function is that it is applicable to data measured in near-field regime or far-field regime. The implementation of the function is simple and does not involve solving any ill-posed problems. The resolution analysis and stability estimate of the indicator function are investigated using the factorization analysis of the far-field operator along with the Funk-Hecke formula. The performance of the method is verified on both simulated and experimental data.