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

This paper concerns a mathematical formulation of the 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 the so-called Multi-Static Response (MSR) matrix and the structure of left-singular vectors linked to the non-zero singular values of the MSR matrix, we construct a relationship between the imaging functional and the Bessel functions of order 0, 1, and 2 of the first kind. We then expound certain properties of MUSIC and present numerical results for several differently chosen smooth arcs.