Shape identification of open sound-hard arcs without priori information in limited-view inverse scattering problem

Abstract

Subspace migration is known as a non-iterative imaging technique for identifying unknown targets in various inverse scattering problems. It has been confirmed that subspace migration is fast, stable, and effective, and can be applied not only to full- but also limited-view inverse problems when a sufficient number of incidents and the corresponding scattered fields are applied and collected. However, the application to the imaging of sound-hard arcs in limited-view problems is somewhat heuristic. Motivated by this, we analyze the imaging functions employed in subspace migration for limited-view inverse scattering problems with and without a priori information of the unit normal vector to the arcs. This is achieved by determining a relationship between an infinite series of Bessel functions with integer order of the first kind and the unit normal vector based on the physical factorization of the multi-static response (MSR), whose elements are measured as a far-field pattern in the presence of arcs. The identified structures explain various intrinsic properties of subspace migration. The results of various numerical simulations with noisy data are exhibited to corroborate the theoretical results.