Abstract
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.
Highlights
Inhomogeneities from Far-FieldIn this study, we consider the fast localization of a set of small electromagnetic inhomogeneities embedded in a homogeneous space from far-field pattern data measured over a limited-aperture configuration
Throughout the paper, we address the mathematical treatment of the scattering of time–harmonic electromagnetic waves from thin infinitely long cylindrical obstacles
As such, based on the singular-value decomposition of the Multistatic Response (MSR) matrix, we generated an appropriate test vector consisting of the incident field at each search point before we used the orthonormal property of the left- and right-singular vectors of the MSR matrix and present a method for designing the indicator functions for localizing the inhomogeneities
Summary
We consider the fast localization of a set of small electromagnetic inhomogeneities embedded in a homogeneous space from far-field pattern data measured over a limited-aperture configuration. The first part of this paper is focused on designing specific indicator functions for permittivity and/or permeability contrast cases to detect the location of small electromagnetic inhomogeneities from the constructed Multistatic Response (MSR) matrix, the elements of which are far-field pattern data for various incident fields [11]. The attendant established theory indicates that the imaging resolution depends on the selection of the applied frequency and that the performance is highly dependent on the selection of the range of incident and observation directions.
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