On the application of MUSIC algorithm for identifying short sound-hard arcs in limited-view inverse acoustic problem

For proper application of the MUltiple SIgnal Classification (MUSIC) algorithm for imaging short, linear sound-hard arcs, one needs a priori information of the unit outward normal vector on each arc. Due to this reason, a set of directions was applied to estimate, which caused the imaging procedure's slowness. Applying a unit vector instead of the estimation is natural to avoid this difficulty. However, no relevant mathematical theory has been developed to explain the various phenomena in simulation results. Here, we consider applying MUSIC without a priori information of the arcs. To this end, we introduce the imaging functions of MUSIC with and without information on the unit outward vector on the arcs. We analyze their mathematical structure by establishing an infinite series of Bessel functions and the range of incident/observation directions and discuss their properties. This is based on the physical factorization of the multistatic response (MSR) matrix that separates the incoming plane-wave information from the unknown density information. Numerical simulation results with noisy data are conducted for small and extended arcs to support the theoretical result. (c) 2022 Elsevier B.V. All rights reserved.