Certain properties of MUSIC-type imaging functional in inverse scattering from an open, sound-hard arc

TL;DR

This paper analyzes the mathematical properties of the MUSIC imaging functional in inverse scattering problems involving open sound-hard arcs, revealing its relationship with Bessel functions and demonstrating its effectiveness through numerical examples.

Contribution

It provides a mathematical formulation of the MUSIC functional for open sound-hard arcs and links it to Bessel functions, enhancing understanding of its properties.

Findings

The MUSIC functional relates to Bessel functions of order 1.

Numerical results confirm the theoretical properties.

The analysis improves the understanding of imaging performance.

Abstract

This paper concerns mathematical formulation of well-known MUltiple SIgnal Classification (MUSIC)-type imaging functional in the inverse scattering problem by an open sound-hard arc. Based on the physical factorization of so-called Multi-Static Response (MSR) matrix and the structure of left-singular vectors liked to the non-zero singular values of MSR matrix, we construct a relationship between imaging functional and Bessel function of order $1$ of the first kind. We then expound certain properties of MUSIC and present numerical results for a number of differently chosen smooth arcs.