# Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber

## TL;DR

This paper investigates why the MUSIC algorithm yields inaccurate target locations when using inappropriate wavenumbers, revealing a theoretical relationship with Bessel functions that explains the phenomenon.

## Contribution

It establishes a theoretical link between MUSIC imaging functionals with wrong wavenumbers and Bessel functions, clarifying the cause of inaccuracies.

## Key findings

- Inaccurate results are linked to the structure of Bessel functions.
- Numerical simulations with noisy data support the theoretical explanation.
- The structure of MUSIC with wrong wavenumbers can be characterized mathematically.

## Abstract

MUltiple SIgnal Classification (MUSIC) is a well-known non-iterative location detection algorithm for small, perfectly conducting cracks in inverse scattering problems. However, when the applied wavenumbers are unknown, inaccurate locations of targets are extracted by MUSIC with inappropriate wavenumbers, a fact that has been confirmed by numerical simulations. To date, the reason behind this phenomenon has not been theoretically investigated. Motivated by this fact, we identify the structure of MUSIC-type imaging functionals with inappropriate wavenumbers by establishing a relationship with Bessel functions of order zero of the first kind. This result explains the reasons for inaccurate results. Various results of numerical simulations with noisy data support the identified structure of MUSIC.