{"title":"电磁反向散射中各向异性周期介质的稳定成像函数","authors":"Dinh-Liem Nguyen, Trung Truong","doi":"10.1137/23m1577080","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. <br/> Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"30 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Stable Imaging Functional for Anisotropic Periodic Media in Electromagnetic Inverse Scattering\",\"authors\":\"Dinh-Liem Nguyen, Trung Truong\",\"doi\":\"10.1137/23m1577080\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. <br/> Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.\",\"PeriodicalId\":51149,\"journal\":{\"name\":\"SIAM Journal on Applied Mathematics\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-07-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1577080\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1577080","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Stable Imaging Functional for Anisotropic Periodic Media in Electromagnetic Inverse Scattering
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1631-1657, August 2024. Abstract. This paper addresses the inverse scattering problem for Maxwell’s equations in three-dimensional anisotropic periodic media. We study a new imaging functional for the fast and robust reconstruction of the shape of anisotropic periodic scatterers from boundary measurements of the scattered field. The implementation of this imaging functional is simple and avoids the need to solve an ill-posed problem. The resolution and stability analysis of the imaging functional is investigated. Results from our numerical study indicate that this imaging functional is more stable than that of the factorization method and more accurate than that of the orthogonality sampling method in reconstructing periodic scatterers.
期刊介绍：
SIAM Journal on Applied Mathematics (SIAP) is an interdisciplinary journal containing research articles that treat scientific problems using methods that are of mathematical interest. Appropriate subject areas include the physical, engineering, financial, and life sciences. Examples are problems in fluid mechanics, including reaction-diffusion problems, sedimentation, combustion, and transport theory; solid mechanics; elasticity; electromagnetic theory and optics; materials science; mathematical biology, including population dynamics, biomechanics, and physiology; linear and nonlinear wave propagation, including scattering theory and wave propagation in random media; inverse problems; nonlinear dynamics; and stochastic processes, including queueing theory. Mathematical techniques of interest include asymptotic methods, bifurcation theory, dynamical systems theory, complex network theory, computational methods, and probabilistic and statistical methods.
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