Imaging of buried obstacles in a two-layered medium with phaseless far-field data

doi:10.1088/1361-6420/abec1d

CSpace > 应用数学研究所

	Imaging of buried obstacles in a two-layered medium with phaseless far-field data
	Li, Long 1; Yang, Jiansheng 1; Zhang, Bo2,3,4 ; Zhang, Haiwen3,5
	2021-05-01
发表期刊	INVERSE PROBLEMS
ISSN	0266-5611
卷号	37 期号:5 页码:26
摘要	This paper is concerned with the inverse problem of reconstructing the location and shape of buried obstacles in the lower half-space of an unbounded two-layered medium in two dimensions from phaseless far-field data. Similarly to the homogenous background medium case, for this problem it is also true that the modulus of the far-field pattern is invariant under translations of the scattering obstacle if only one plane wave is used as the incident field, and thus it is impossible to determine the location of the obstacle from such phaseless far-field data. Based on the idea of using superpositions of two plane waves with different directions as the incident fields, a direct imaging algorithm is developed in this paper to locate the position of small anomalies with the intensity of the far-field pattern measured in the upper half-space. This is a nontrivial extension of our previous work (2018 Inverse Problems 34 104005) from the homogenous background medium case to the two-layered background medium case. Both the limited aperture measurement data and the presence of the two-layered background medium lead to difficulties in the theoretical analysis of the proposed imaging algorithm. To overcome the difficulties we employ the theory of oscillatory integrals. Further, with the aid of the imaging algorithm, a recursive Newton-type iteration algorithm in frequencies is proposed to reconstruct both the location and shape of extended obstacles. Finally, numerical experiments are presented to illustrate the feasibility of our algorithms.
关键词	two-layered medium buried obstacle phaseless far-field data direct imaging method recursive Newton-type iteration algorithm
DOI	10.1088/1361-6420/abec1d
收录类别	SCI
语种	英语
资助项目	NNSF of China[11961141007] ; NNSF of China[61520106004] ; NNSF of China[11871466] ; Microsoft Research of Asia ; Youth Innovation Promotion Association CAS
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000640393500001
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58503
专题	应用数学研究所
通讯作者	Zhang, Haiwen
作者单位	1.Peking Univ, Sch Math Sci, LMAM, Beijing 100871, Peoples R China 2.Chinese Acad Sci, LSEC, NCMIS, Beijing 100190, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 5.Chinese Acad Sci, NCMIS, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Li, Long,Yang, Jiansheng,Zhang, Bo,et al. Imaging of buried obstacles in a two-layered medium with phaseless far-field data[J]. INVERSE PROBLEMS,2021,37(5):26.
APA	Li, Long,Yang, Jiansheng,Zhang, Bo,&Zhang, Haiwen.(2021).Imaging of buried obstacles in a two-layered medium with phaseless far-field data.INVERSE PROBLEMS,37(5),26.
MLA	Li, Long,et al."Imaging of buried obstacles in a two-layered medium with phaseless far-field data".INVERSE PROBLEMS 37.5(2021):26.