Certain properties of MUSIC-type imaging functional in inverse scattering from an open, sound-hard arc
This work provides a theoretical foundation for MUSIC imaging in a specific inverse scattering problem, but the results are incremental and limited to the sound-hard arc case.
The paper mathematically formulates the MUSIC-type imaging functional for inverse scattering from an open sound-hard arc, deriving a relationship with the Bessel function of order 1 and demonstrating properties through numerical examples.
This paper concerns mathematical formulation of 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 so-called Multi-Static Response (MSR) matrix and the structure of left-singular vectors liked to the non-zero singular values of MSR matrix, we construct a relationship between imaging functional and Bessel function of order $1$ of the first kind. We then expound certain properties of MUSIC and present numerical results for a number of differently chosen smooth arcs.