INVERSE ELECTROMAGNETIC SOURCE SCATTERING PROBLEMS WITH MULTIFREQUENCY SPARSE PHASED AND PHASELESS FAR FIELD DATA

doi:10.1137/19M1256518

CSpace > 应用数学研究所

	INVERSE ELECTROMAGNETIC SOURCE SCATTERING PROBLEMS WITH MULTIFREQUENCY SPARSE PHASED AND PHASELESS FAR FIELD DATA
	Ji, Xia1 ; Liu, Xiaodong2
	2019
发表期刊	SIAM JOURNAL ON SCIENTIFIC COMPUTING
ISSN	1064-8275
卷号	41 期号:6 页码:B1368-B1388
摘要	This paper is concerned with uniqueness, phase retrieval, and shape reconstruction methods for solving inverse electromagnetic source scattering problems with multifrequency sparse phased or phaseless far field data. With the phased data, we show that the smallest strip containing the source support with the observation direction as the normal can be uniquely determined by the multifrequency far field pattern at a single observation direction. A phased direct sampling method is also proposed to reconstruct the strip. The phaseless far field data is closely related to the outward energy flux, which can be measured more easily in practice. We show that the phaseless far field data is invariant under the translation of the sources, which implies that the location of the sources cannot be uniquely recovered by the data. To solve this problem, we consider simultaneously the scattering of magnetic dipoles with one fixed source point and at most three scattering strengths. With this technique, a fast and stable phase retrieval approach is proposed based on a simple geometrical result which provides a stable reconstruction of a point in the plane from three distances to the given points. A novel phaseless direct sampling method is also proposed to reconstruct the strip. The phase retrieval approach can also be combined with the phased direct sampling method to reconstruct the strip. Finally, to obtain a source support, we just need to superimpose the indicators with respect to the sparse observation directions. Extended numerical examples in three dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed phase retrieval approach and direct sampling methods.
关键词	electromagnetic source scattering phaseless far field data uniqueness phase retrieval direct sampling methods
DOI	10.1137/19M1256518
收录类别	SCI
语种	英语
资助项目	NNSF of China[11271018] ; NNSF of China[11971468] ; NNSF of China[91630313] ; NNSF of China[11571355] ; NNSF of China[11971701] ; National Centre for Mathematics and Interdisciplinary Sciences, CAS ; Youth Innovation Promotion Association, CAS
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000549131500030
出版者	SIAM PUBLICATIONS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51796
专题	应用数学研究所计算数学与科学工程计算研究所
通讯作者	Ji, Xia
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Beijing 100190, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Ji, Xia,Liu, Xiaodong. INVERSE ELECTROMAGNETIC SOURCE SCATTERING PROBLEMS WITH MULTIFREQUENCY SPARSE PHASED AND PHASELESS FAR FIELD DATA[J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING,2019,41(6):B1368-B1388.
APA	Ji, Xia,&Liu, Xiaodong.(2019).INVERSE ELECTROMAGNETIC SOURCE SCATTERING PROBLEMS WITH MULTIFREQUENCY SPARSE PHASED AND PHASELESS FAR FIELD DATA.SIAM JOURNAL ON SCIENTIFIC COMPUTING,41(6),B1368-B1388.
MLA	Ji, Xia,et al."INVERSE ELECTROMAGNETIC SOURCE SCATTERING PROBLEMS WITH MULTIFREQUENCY SPARSE PHASED AND PHASELESS FAR FIELD DATA".SIAM JOURNAL ON SCIENTIFIC COMPUTING 41.6(2019):B1368-B1388.