Asymptotic properties of MUSIC-type imaging in two-dimensional inverse scattering from thin electromagnetic inclusions

TL;DR

This paper analyzes the asymptotic behavior of the MUSIC algorithm for imaging thin electromagnetic inclusions in 2D, revealing its connection to Bessel functions and providing insights into its structure.

Contribution

It establishes a theoretical link between MUSIC imaging functional and Bessel functions for thin inclusions, enhancing understanding of its asymptotic properties.

Findings

MUSIC functional relates to Bessel functions of integer order.

Asymptotic expansion formulas are derived for thin inclusions.

Numerical examples support the theoretical structure.

Abstract

The main purpose of this paper is to study the structure of the well-known non-iterative MUltiple SIgnal Classification (MUSIC) algorithm for identifying the shape of extended electromagnetic inclusions of small thickness located in a two-dimensional homogeneous space. We construct a relationship between the MUSIC-type imaging functional for thin inclusions and the Bessel function of integer order of the first kind. Our construction is based on the structure of the left singular vectors of the collected multistatic response matrix whose elements are the measured far-field pattern and the asymptotic expansion formula in the presence of thin inclusions. Some numerical examples are shown to support the constructed MUSIC structure.