Structural Behavior of the Music-Type Algorithm for Imaging Perfectly Conducting Cracks

We consider MUltiple SIgnal Classification (MUSIC)-type imaging of perfectly conducting cracks arising in inverse scattering problems. We first explore the structure of a MUSIC-type imaging function by finding a relationship between it and the Bessel function of order zero of the first kind. Then, we design multi-frequency based MUSIC-type imaging in order to improve the traditional one, and establish a relationship with the Bessel function of integer order of the first kind. Some numerical experiments are presented to support the results of our investigation.