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 |
DOI | 10.1088/1361-6420/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
浏览0
下载0
收藏0
其他版本
除非特别说明,本系统中所有内容都受版权保护,并保留所有权利。