Fast identification of small perfectly conducting cracks without diagonal elements of multi-static response matrix

Abstract

ABSTRACTWe explore mathematical structures of indicator functions used in subspace migration to identify the location of a set of perfectly conducting cracks with small lengths when the diagonal elements of a Multi-Static Response (MSR) matrix cannot be obtained. By using the asymptotic formula for the presence of cracks and the structure of the singular vectors linked to the nonzero singular values of the MSR matrix, we prove that the indicator function can be represented by a Bessel function of order zero of the first kind and the total number of incident and observation directions in a full-view inverse scattering problem. We also present experimental results of numerical simulations with noisy data to validate our findings.