View in EDS

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

Saved in:
Bibliographic Details
Title: Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem
Authors: Won-Kwang Park
Source: Mathematics, Vol 9, Iss 2087, p 2087 (2021)
Publisher Information: MDPI AG
Publication Year: 2021
Collection: Directory of Open Access Journals: DOAJ Articles
Subject Terms: fast localization, sampling-type algorithm, small electromagnetic inhomogeneities, multistatic response matrix, simulation results, Mathematics, QA1-939
Description: 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.
Document Type: article in journal/newspaper
Language: English
Relation: https://www.mdpi.com/2227-7390/9/17/2087; https://doaj.org/toc/2227-7390; https://doaj.org/article/c14d02bac1a4469fbc6eb0683a8bb31b
DOI: 10.3390/math9172087
Availability: https://doi.org/10.3390/math9172087
https://doaj.org/article/c14d02bac1a4469fbc6eb0683a8bb31b
Accession Number: edsbas.5C4F265
Database: BASE
Description
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.
DOI:10.3390/math9172087