Reconstruction of small and extended scatterers with a conductive boundary using far-field data

TL;DR

This paper develops qualitative methods for reconstructing small and extended isotropic scatterers with conductive boundaries from far-field data at a fixed frequency, using asymptotic analysis, MUSIC, and factorization techniques.

Contribution

It introduces new asymptotic expansions and a factorization approach for reconstructing scatterers, enhancing existing qualitative inverse scattering methods.

Findings

Asymptotic expansion enables MUSIC algorithm application for small scatterers.

New factorization of the far-field operator improves resolution analysis for extended scatterers.

Numerical experiments validate the theoretical reconstruction methods in 2D.

Abstract

In this paper, we consider the inverse shape problem of recovering small and extended isotropic scatterers with a conductive boundary condition. Here, we assume that the measured far-field data is known at a fixed wave number. We will provide qualitative reconstruction methods for recovering either small or extended scatterers. For the case of small scatterers, we model this by a region(possibly with multiple components) with small volume. We derive an asymptotic expansion for the far-field pattern which will allow us to study the MUSIC algorithm for solving the problem. In the case of an extended scatterer, we derive a new factorization of the far-field operator. This is then used to provide the resolution analysis for a direct sampling method. The theoretical results are verified with some numerical experiments in 2--dimensions.