Application of MUSIC algorithm for a fast identification of small perfectly conducting cracks in limited-aperture inverse scattering problem

Abstract

In this study, we investigate MUltiple SIgnal Classification (MUSIC) operated at a fixed frequency for identifying the locations of short, linear perfectly conducting cracks in limited-aperture inverse scattering problem. At present, the so-called multi-static response (MSR) matrix whose elements are measured far-field pattern data is neither symmetric nor Hermitian, a projection operator onto the noise subspace cannot be defined using the conventional method, so the imaging function cannot be designed. Motivated by this fact, we first propose a novel MUSIC imaging function in limited-aperture inverse scattering problem. This is based on the asymptotic expansion formula for far-field patterns in the presence of small cracks and the structure of singular vectors associated with nonzero singular values of the MSR matrix. Next, the new imaging function was analyzed by establishing a relationship with an infinite series of the Bessel function of the integer order of the first kind and ranges of incident and observation directions. We then observe some properties of MUSIC in limited-aperture problems and show that the proposed imaging function is a generalization of full- and limited-view problems. We finally validate the feasibility and limitation of the proposed MUSIC imaging function through numerical simulation results using synthetic and real data.