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Recovering scattering obstacles by multi-frequency phaseless far-field data
Zhang, Bo1,2,3; Zhang, Haiwen4
2017-09-15
Source PublicationJOURNAL OF COMPUTATIONAL PHYSICS
ISSN0021-9991
Volume345Pages:58-73
AbstractIt is well known that the modulus of the far-field pattern (or phaseless far-field pattern) is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, so the shape but not the location of the obstacle can be recovered from the phaseless far-field data. This paper aims to devise an approach to break the translation invariance property of the phaseless far-field pattern. To this end, we make use of the superposition of two plane waves rather than one plane wave as the incident field. In this paper, it is mathematically proved that the translation invariance property of the phaseless far-field pattern can indeed be broken if superpositions of two plane waves are used as the incident fields for all wave numbers in a finite interval. Furthermore, a recursive Newton type iteration algorithm in frequencies is also developed to numerically recover both the location and the shape of the obstacle simultaneously from multi-frequency phaseless far field data. Numerical examples are also carried out to illustrate the validity of the approach and the effectiveness of the inversion algorithm. (C) 2017 Elsevier Inc. All rights reserved.
KeywordInverse obstacle scattering Phaseless far-field pattern Recursive Newton iteration method Recovery of obstacles Incident plane waves Multiple frequency data
DOI10.1016/j.jcp.2017.05.022
Language英语
Funding ProjectNNSF of China[91430102] ; NNSF of China[91630309] ; NNSF of China[61379093] ; NNSF of China[11501558] ; National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS Research AreaComputer Science ; Physics
WOS SubjectComputer Science, Interdisciplinary Applications ; Physics, Mathematical
WOS IDWOS:000405974900005
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Citation statistics
Cited Times:16[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26196
Collection应用数学研究所
Affiliation1.Chinese Acad Sci, AMSS, LSEC, Beijing 100190, Peoples R China
2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Chinese Acad Sci, Inst Appl Math, AMSS, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Zhang, Bo,Zhang, Haiwen. Recovering scattering obstacles by multi-frequency phaseless far-field data[J]. JOURNAL OF COMPUTATIONAL PHYSICS,2017,345:58-73.
APA Zhang, Bo,&Zhang, Haiwen.(2017).Recovering scattering obstacles by multi-frequency phaseless far-field data.JOURNAL OF COMPUTATIONAL PHYSICS,345,58-73.
MLA Zhang, Bo,et al."Recovering scattering obstacles by multi-frequency phaseless far-field data".JOURNAL OF COMPUTATIONAL PHYSICS 345(2017):58-73.
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