中国科学院机构知识库网格
Chinese Academy of Sciences Institutional Repositories Grid
Inverse elastic scattering problems with phaseless far field data

文献类型:期刊论文

作者Ji,Xia2; Liu,Xiaodong1
刊名Inverse Problems
出版日期2019-10-03
卷号35期号:11
ISSN号0266-5611
关键词elastic scattering phaseless far field data uniqueness phase retrieval direct sampling methods
DOI10.1088/1361-6420/ab2a35
英文摘要Abstract This paper is concerned with uniqueness, phase retrieval and shape reconstruction methods for inverse elastic scattering problems with phaseless far field data. The phaseless far field data is closely related to the outward energy flux, which is easily measured in practice. Systematically, we study two basic models, i.e. inverse scattering of plane waves by rigid bodies and inverse scattering of sources with compact support. For both models, we show that the phaseless far field data is invariant under translation of the underlying scattering objects, which implies that the location of the objects can not be uniquely recovered by the data. To solve this problem, we consider simultaneously the incident point sources with one fixed source point and at most three scattering strengths. With this technique, we establish some uniqueness results for source scattering problem with multi-frequency phaseless far field data. Furthermore, a fast and stable phase retrieval approach is proposed based on a simple geometric result which provides a stable reconstruction of a point in the plane from three distances to given points. Difficulties arise for inverse scattering by rigid bodies due to the additional unknown far field pattern of the point sources. To overcome this difficulty, we introduce an artificial rigid body into the system and show that the underlying rigid bodies can be uniquely determined by the corresponding phaseless far field data at a fixed frequency. Noting that the far field pattern of the scattered field corresponding to point sources is very small if the source point is far away from the scatterers, we propose an appropriate phase retrieval method for obstacle scattering problems, without using the artificial rigid body. Finally, we propose several sampling methods for shape reconstruction with phaseless far field data directly. For inverse obstacle scattering problems, two different direct sampling methods are proposed with data at a fixed frequency. For inverse source scattering problems, we introduce two direct sampling methods for source supports with sparse multi-frequency data. The phase retrieval techniques are also combined with the classical sampling methods for the shape reconstructions. Extended numerical examples in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed phase retrieval techniques and sampling methods.
语种英语
出版者IOP Publishing
WOS记录号IOP:0266-5611-35-11-AB2A35
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/33326]  
专题应用数学研究所
计算数学与科学工程计算研究所
作者单位1.Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190 Beijing, People’s Republic of China
2.LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, People’s Republic of China
推荐引用方式
GB/T 7714
Ji,Xia,Liu,Xiaodong. Inverse elastic scattering problems with phaseless far field data[J]. Inverse Problems,2019,35(11).
APA Ji,Xia,&Liu,Xiaodong.(2019).Inverse elastic scattering problems with phaseless far field data.Inverse Problems,35(11).
MLA Ji,Xia,et al."Inverse elastic scattering problems with phaseless far field data".Inverse Problems 35.11(2019).

入库方式: OAI收割

来源:数学与系统科学研究院

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