Invisibility enables super-visibility in electromagnetic imaging

TL;DR

This paper introduces a novel electromagnetic imaging method leveraging interior resonant modes and transmission eigenfunctions to achieve super-resolution imaging of anisotropic media scatterers.

Contribution

The paper develops a new inverse scattering scheme using interior resonant modes and transmission eigenfunctions, with rigorous theory and numerical validation.

Findings

Effective determination of interior Maxwell transmission eigenvalues

Accurate shape reconstruction of scatterers

Super-resolution imaging results

Abstract

This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three phases. First, we determine the interior Maxwell transmission eigenvalues of the scatterer from a family of far-field data by the mechanism of the linear sampling method. Next, we determine the corresponding transmission eigenfunctions by solving a constrained optimization problem. Finally, based on both global and local geometric properties of the transmission eigenfunctions, we design an imaging functional which can be used to determine the shape of the medium scatterer. We provide rigorous theoretical basis for our method. Numerical experiments verify the effectiveness, better accuracy and super-resolution results of the proposed scheme.