Stable Reconstruction of Anisotropic Objects from Near-Field Electromagnetic Data

TL;DR

This paper develops stable, efficient imaging functionals for reconstructing anisotropic objects from near-field electromagnetic data, applicable to Helmholtz and Maxwell equations, with proven stability and demonstrated numerical success.

Contribution

It introduces novel imaging functionals that are simple to implement, avoid solving ill-posed problems, and provide stable reconstructions for anisotropic objects in electromagnetic inverse scattering.

Findings

Imaging functionals are stable under noisy data.

Numerical examples confirm effectiveness and accuracy.

Resolution analysis is based on Green's formula.

Abstract

This paper addresses the electromagnetic inverse scattering problem of determining the location and shape of anisotropic objects from near-field data. We investigate both cases involving the Helmholtz equation and Maxwell's equations for this inverse problem. Our study focuses on developing efficient imaging functionals that enable a fast and stable recovery of the anisotropic object. The implementation of the imaging functionals is simple and avoids the need to solve an ill-posed problem. The resolution analysis of the imaging functionals is conducted using the Green representation formula. Furthermore, we establish stability estimates for these imaging functionals when noise is present in the data. To illustrate the effectiveness of the methods, we present numerical examples showcasing their performance.