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Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency
Zhang, Bo1,2,3; Zhang, Haiwen2,4
2018-10-01
Source PublicationINVERSE PROBLEMS
ISSN0266-5611
Volume34Issue:10Pages:24
AbstractThis paper is concerned with the inverse obstacle scattering problem with phaseless far-field data at a fixed frequency. The main difficulty of this problem is the so-called translation invariance property of the modulus of the far-field pattern or the phaseless far-field pattern generated by one plane wave as the incident field, which means that the location of the obstacle cannot be recovered from such phaseless far-field data at a fixed frequency. It was recently proved in our previous work Xu et al 2018 (SIAM J. Appl. Math. 78 1737-53) that the obstacle can be uniquely determined by the phaseless far-field patterns generated by infinitely many sets of superpositions of two plane waves with different directions at a fixed frequency if the obstacle is a priori known to be a sound-soft or an impedance obstacle with real-valued impedance function. The purpose of this paper is to develop a direct imaging algorithm to reconstruct the location and shape of the obstacle from the phaseless farfield data corresponding to infinitely many sets of superpositions of two plane waves with a fixed frequency as the incident fields. Our imaging algorithm only involves the calculation of the products of the measurement data with two exponential functions at each sampling point and is thus fast and easy to implement. Further, the proposed imaging algorithm does not need to know the type of boundary conditions on the obstacle in advance and is capable to reconstruct multiple obstacles with different boundary conditions. Numerical experiments are also carried out to illustrate that our imaging method is stable, accurate and robust to noise.
Keywordinverse scattering Helmholtz equation phaseless far-field data direct imaging method
DOI10.1088/1361-6420/aad81f
Language英语
Funding ProjectNNSF of China[91630309] ; NNSF of China[11501558] ; NNSF of China[11571355]
WOS Research AreaMathematics ; Physics
WOS SubjectMathematics, Applied ; Physics, Mathematical
WOS IDWOS:000442445400001
PublisherIOP PUBLISHING LTD
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/31114
Collection应用数学研究所
Affiliation1.Chinese Acad Sci, NCMIS, LSEC, 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
Recommended Citation
GB/T 7714
Zhang, Bo,Zhang, Haiwen. Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency[J]. INVERSE PROBLEMS,2018,34(10):24.
APA Zhang, Bo,&Zhang, Haiwen.(2018).Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency.INVERSE PROBLEMS,34(10),24.
MLA Zhang, Bo,et al."Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency".INVERSE PROBLEMS 34.10(2018):24.
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