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Imaging of buried obstacles in a two-layered medium with phaseless far-field data
Li, Long1; Yang, Jiansheng1; Zhang, Bo2,3,4; Zhang, Haiwen3,5
2021-05-01
Source PublicationINVERSE PROBLEMS
ISSN0266-5611
Volume37Issue:5Pages:26
AbstractThis 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.
Keywordtwo-layered medium buried obstacle phaseless far-field data direct imaging method recursive Newton-type iteration algorithm
DOI10.1088/1361-6420/abec1d
Indexed BySCI
Language英语
Funding ProjectNNSF of China[11961141007] ; NNSF of China[61520106004] ; NNSF of China[11871466] ; Microsoft Research of Asia ; Youth Innovation Promotion Association CAS
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000640393500001
PublisherIOP PUBLISHING LTD
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/58503
Collection应用数学研究所
Corresponding AuthorZhang, Haiwen
Affiliation1.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
Recommended Citation
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.
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