Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem

In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in the limited-aperture inverse scattering problem. For this purpose, we designed an indicator function based on the structure of left- and right-singular vectors of a multistatic response matrix, the elements of which were measured far-field pattern data. We then rigorously investigated the mathematical structure of the indicator function in terms of purely dielectric permittivity and magnetic permeability contrast cases by establishing a relationship with an infinite series of Bessel functions of an integer order of the first kind and a range of incident and observation directions before exploring various intrinsic properties of the algorithm, including its feasibility and limitations. Simulation results with synthetic data corrupted by random noise are presented to support the theoretical results.