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UNIQUENESS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS FAR-FIELD DATA AT A FIXED FREQUENCY. II
Xu, Xiaoxu1,2; Zhang, Bo1,2,3; Zhang, Haiwen1
2018
Source PublicationSIAM JOURNAL ON APPLIED MATHEMATICS
ISSN0036-1399
Volume78Issue:6Pages:3024-3039
AbstractThis paper is concerned with uniqueness in inverse acoustic scattering with phaseless far-field data at a fixed frequency. In our previous work [SIAM T. Appi. Math., 78 (2018), pp. 1737-1753], by utilizing spectral properties of the far-field operator we proved for the first time that the obstacle and the index of refraction of an inhomogeneous medium 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 under the a priori assumption that the obstacle is known to be a sound-soft or nonabsorbing impedance obstacle and the index of refraction n of the inhomogeneous medium is real-valued and satisfies that either n - 1 > c(1) or n - 1 < -c(1) in the support of n - 1 for some positive constant c(1) . In this paper, we remove the a priori assumption on the obstacle and the index of refraction of the inhomogeneous medium by adding a reference ball to the scattering system together with a simpler method of using Rellich's lemma and Green's representation formula for the scattering solutions. Further, our new method is also used to prove uniqueness in determining a locally rough surface from the phaseless far-field patterns corresponding to infinitely many sets of superpositions of two plane waves with different directions as the incident fields at a fixed frequency.
Keyworduniqueness inverse scattering phaseless far-field pattern Dirichlet boundary conditions impedance boundary conditions inhomogeneous medium locally rough surfaces
DOI10.1137/18M1196820
Language英语
Funding ProjectNNSF of China[91630309] ; NNSF of China[11501558] ; NNSF of China[11571355] ; National Center for Mathematics and Interdisciplinary Sciences, CAS
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000453783800005
PublisherSIAM PUBLICATIONS
Citation statistics
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/32023
Collection应用数学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
3.Chinese Acad Sci, LSEC, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Xu, Xiaoxu,Zhang, Bo,Zhang, Haiwen. UNIQUENESS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS FAR-FIELD DATA AT A FIXED FREQUENCY. II[J]. SIAM JOURNAL ON APPLIED MATHEMATICS,2018,78(6):3024-3039.
APA Xu, Xiaoxu,Zhang, Bo,&Zhang, Haiwen.(2018).UNIQUENESS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS FAR-FIELD DATA AT A FIXED FREQUENCY. II.SIAM JOURNAL ON APPLIED MATHEMATICS,78(6),3024-3039.
MLA Xu, Xiaoxu,et al."UNIQUENESS IN INVERSE SCATTERING PROBLEMS WITH PHASELESS FAR-FIELD DATA AT A FIXED FREQUENCY. II".SIAM JOURNAL ON APPLIED MATHEMATICS 78.6(2018):3024-3039.
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