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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...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2019
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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 |
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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 |