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

doi:10.1137/19M1280612

CSpace > 应用数学研究所

	AN APPROXIMATE FACTORIZATION METHOD FOR INVERSE ACOUSTIC SCATTERING WITH PHASELESS TOTAL-FIELD DATA
	Zhang, Bo1,2,3 ; Zhang, Haiwen2,4,5
	2020
发表期刊	SIAM JOURNAL ON APPLIED MATHEMATICS
ISSN	0036-1399
卷号	80 期号:5 页码:2271-2298
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.
关键词	inverse acoustic scattering approximate factorization method phaseless total-field data asymptotic behavior of phaseless total-field operator
DOI	10.1137/19M1280612
收录类别	SCI
语种	英语
资助项目	National Natural Science Foundation of China[11871466] ; National Natural Science Foundation of China[91630309]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000584685100012
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/52520
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.