Appearance of inaccurate results in the MUSIC algorithm with inappropriate wavenumber
For researchers using MUSIC in inverse scattering, this explains a known failure mode, but the contribution is incremental as it only provides theoretical justification for an observed phenomenon.
The paper identifies the theoretical reason why the MUSIC algorithm yields inaccurate target locations when applied with inappropriate wavenumbers, establishing a relationship with Bessel functions. Numerical simulations confirm the identified structure.
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.