Fast imaging of scattering obstacles from phaseless far-field measurements at a fixed frequency

doi:10.1088/1361-6420/aad81f

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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
发表期刊	INVERSE PROBLEMS
ISSN	0266-5611
卷号	34 期号:10 页码:24
摘要	This 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.
关键词	inverse scattering Helmholtz equation phaseless far-field data direct imaging method
DOI	10.1088/1361-6420/aad81f
语种	英语
资助项目	NNSF of China[91630309] ; NNSF of China[11501558] ; NNSF of China[11571355]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000442445400001
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/31114
专题	应用数学研究所
通讯作者	Zhang, Bo
作者单位	1.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
推荐引用方式 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.