A Direct Sampling Method for Inverse Electromagnetic Medium Scattering

TL;DR

This paper introduces a new direct sampling method for inverse electromagnetic scattering that efficiently estimates the shape and support of scatterers from near-field data, even with noisy measurements.

Contribution

The paper develops a novel direct sampling approach based on electromagnetic scattering analysis, requiring only inner products with fundamental solutions, making it computationally efficient and noise-tolerant.

Findings

Method works with single incident field

Provides reliable support estimates in noisy data

Effective in 2D and 3D scenarios

Abstract

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric or magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. The method is applicable even with one incident field and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence it is strictly direct, computationally very efficient, and highly tolerant to the presence of noise in the data. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates of one single and multiple scatterers in case of both exact and highly noisy data.