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AN APPROXIMATE FACTORIZATION METHOD FOR INVERSE ACOUSTIC SCATTERING WITH PHASELESS TOTAL-FIELD DATA

文献类型：期刊论文

作者Zhang, Bo1,2,3; Zhang, Haiwen2,4,5
刊名SIAM JOURNAL ON APPLIED MATHEMATICS
出版日期2020
卷号80期号:5页码:2271-2298
关键词inverse acoustic scattering approximate factorization method phaseless total-field data asymptotic behavior of phaseless total-field operator
ISSN号0036-1399
DOI10.1137/19M1280612
英文摘要This paper is concerned with the inverse acoustic scattering problem with phaseless total-field data at a fixed frequency. An approximate factorization method is developed to numerically reconstruct both the location and shape of the unknown scatterer from the phaseless total-field data generated by incident plane waves at a fixed frequency and measured on the circle partial derivative B-R with a sufficiently large radius R. The theoretical analysis of our method is based on the asymptotic property in the operator norm from H-1/2 (S-1) to H-1/2 (S-1) of the phaseless total-field operator defined in terms of the phaseless total-field data measured on partial derivative B-R with large enough R, where H-s (S-1) is a Sobolev space on the unit circle S-1 for real number s, together with the factorization of a modified far-field operator. The asymptotic property of the phaseless total-field operator is also established in this paper with the theory of oscillatory integrals. The unknown scatterer can be either an impenetrable obstacle of sound-soft, sound-hard, or impedance type, or an inhomogeneous medium with a compact support, and the proposed inversion algorithm does not need to know the boundary condition of the unknown obstacle in advance. Numerical examples are also carried out to demonstrate the effectiveness of our inversion method. To the best of our knowledge, this is the first attempt to develop a factorization type method for inverse scattering problems with phaseless data.
资助项目National Natural Science Foundation of China[11871466] ; National Natural Science Foundation of China[91630309]
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000584685100012
出版者SIAM PUBLICATIONS
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/52519]  
专题应用数学研究所
通讯作者Zhang, Haiwen
作者单位1.Chinese Acad Sci, LSEC, NCMIS, Beijing 100190, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
4.Chinese Acad Sci, NCMIS, Beijing 100190, Peoples R China
5.Univ Gottingen, Inst Numer & Appl Math, Lotzestr 16-18, D-37083 Gottingen, Germany
推荐引用方式
GB/T 7714		 Zhang, Bo,Zhang, Haiwen. AN APPROXIMATE FACTORIZATION METHOD FOR INVERSE ACOUSTIC SCATTERING WITH PHASELESS TOTAL-FIELD DATA[J]. SIAM JOURNAL ON APPLIED MATHEMATICS,2020,80(5):2271-2298.
APA Zhang, Bo,&Zhang, Haiwen.(2020).AN APPROXIMATE FACTORIZATION METHOD FOR INVERSE ACOUSTIC SCATTERING WITH PHASELESS TOTAL-FIELD DATA.SIAM JOURNAL ON APPLIED MATHEMATICS,80(5),2271-2298.
MLA Zhang, Bo,et al."AN APPROXIMATE FACTORIZATION METHOD FOR INVERSE ACOUSTIC SCATTERING WITH PHASELESS TOTAL-FIELD DATA".SIAM JOURNAL ON APPLIED MATHEMATICS 80.5(2020):2271-2298.

入库方式： OAI收割

来源：数学与系统科学研究院

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