Robust multifrequency imaging with MUSIC

TL;DR

This paper analyzes the robustness of the MUSIC algorithm in multifrequency active array imaging, demonstrating its effectiveness under certain conditions and providing theoretical and numerical validation.

Contribution

It extends MUSIC's application to multifrequency imaging with arbitrary arrays, establishing conditions for robustness and offering theoretical insights and numerical evidence.

Findings

MUSIC is robust to noise when targets are well separated.

The algorithm's performance depends on controlled parameters like excitations.

Theoretical results are supported by numerical experiments.

Abstract

In this paper, we study the MUltiple SIgnal Classification (MUSIC) algorithm often used to image small targets when multiple measurement vectors are available. We show that this algorithm may be used when the imaging problem can be cast as a linear system that admits a special factorization. We discuss several active array imaging configurations where this factorization is exact, as well as other configurations where the factorization only holds approximately and, hence, the results provided by MUSIC deteriorate. We give special attention to the most general setting where an active array with an arbitrary number of transmitters and receivers uses signals of multiple frequencies to image the targets. This setting provides all the possible diversity of information that can be obtained from the illuminations. We give a theorem that shows that MUSIC is robust with respect to additive noise provided that the targets are well separated. The theorem also shows the relevance of using appropriate sets of controlled parameters, such as excitations, to form the images with MUSIC robustly. We present numerical experiments that support our theoretical results.