Cargando…

Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems

Inverse scattering problems (ISPs) stand at the center of many important imaging applications, such as geophysical explorations, industrial non-destructive testing, bio-medical imaging, etc. Recently, a new type of contraction integral equation for inversion (CIE-I) has been proposed to tackle the t...

Descripción completa

Detalles Bibliográficos
Autores principales: Zhong, Yu, Xu, Kuiwen
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2019
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8320915/
https://www.ncbi.nlm.nih.gov/pubmed/34460475
http://dx.doi.org/10.3390/jimaging5020027
_version_ 1783730726843187200
author Zhong, Yu
Xu, Kuiwen
author_facet Zhong, Yu
Xu, Kuiwen
author_sort Zhong, Yu
collection PubMed
description Inverse scattering problems (ISPs) stand at the center of many important imaging applications, such as geophysical explorations, industrial non-destructive testing, bio-medical imaging, etc. Recently, a new type of contraction integral equation for inversion (CIE-I) has been proposed to tackle the two-dimensional electromagnetic ISPs, in which the usually employed Lippmann–Schwinger integral equation (LSIE) is transformed into a new form with a modified medium contrast via a contraction mapping. With the CIE-I, the multiple scattering effects, i.e., the physical reason for the nonlinearity in the ISPs, is substantially suppressed in estimating the modified contrast, without compromising physical modeling. In this paper, we firstly propose to implement this new CIE-I for the three-dimensional ISPs. With the help of the FFT type twofold subspace-based optimization method (TSOM), when handling the highly nonlinear problems with strong scatterers, those with higher contrast and/or larger dimensions (in terms of wavelengths), the performance of the inversions with CIE-I is much better than the ones with the LSIE, wherein inversions usually converge to local minima that may be far away from the solution. In addition, when handling the moderate scatterers (those the LSIE modeling can still handle), the convergence speed of the proposed method with CIE-I is much faster than the one with the LSIE. Secondly, we propose to relax the contraction mapping condition, i.e., different contraction mappings are used in updating contrast sources and contrast, and we find that the convergence can be further accelerated. Several numerical tests illustrate the aforementioned interests.
format Online
Article
Text
id pubmed-8320915
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher MDPI
record_format MEDLINE/PubMed
spelling pubmed-83209152021-08-26 Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems Zhong, Yu Xu, Kuiwen J Imaging Article Inverse scattering problems (ISPs) stand at the center of many important imaging applications, such as geophysical explorations, industrial non-destructive testing, bio-medical imaging, etc. Recently, a new type of contraction integral equation for inversion (CIE-I) has been proposed to tackle the two-dimensional electromagnetic ISPs, in which the usually employed Lippmann–Schwinger integral equation (LSIE) is transformed into a new form with a modified medium contrast via a contraction mapping. With the CIE-I, the multiple scattering effects, i.e., the physical reason for the nonlinearity in the ISPs, is substantially suppressed in estimating the modified contrast, without compromising physical modeling. In this paper, we firstly propose to implement this new CIE-I for the three-dimensional ISPs. With the help of the FFT type twofold subspace-based optimization method (TSOM), when handling the highly nonlinear problems with strong scatterers, those with higher contrast and/or larger dimensions (in terms of wavelengths), the performance of the inversions with CIE-I is much better than the ones with the LSIE, wherein inversions usually converge to local minima that may be far away from the solution. In addition, when handling the moderate scatterers (those the LSIE modeling can still handle), the convergence speed of the proposed method with CIE-I is much faster than the one with the LSIE. Secondly, we propose to relax the contraction mapping condition, i.e., different contraction mappings are used in updating contrast sources and contrast, and we find that the convergence can be further accelerated. Several numerical tests illustrate the aforementioned interests. MDPI 2019-02-08 /pmc/articles/PMC8320915/ /pubmed/34460475 http://dx.doi.org/10.3390/jimaging5020027 Text en © 2019 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Zhong, Yu
Xu, Kuiwen
Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems
title Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems
title_full Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems
title_fullStr Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems
title_full_unstemmed Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems
title_short Contraction Integral Equation for Three-Dimensional Electromagnetic Inverse Scattering Problems
title_sort contraction integral equation for three-dimensional electromagnetic inverse scattering problems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8320915/
https://www.ncbi.nlm.nih.gov/pubmed/34460475
http://dx.doi.org/10.3390/jimaging5020027
work_keys_str_mv AT zhongyu contractionintegralequationforthreedimensionalelectromagneticinversescatteringproblems
AT xukuiwen contractionintegralequationforthreedimensionalelectromagneticinversescatteringproblems