Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data
文献类型：期刊论文
| 作者 | Xu, Xiaoxu1,2; Zhang, Bo1,2,4 ; Zhang, Haiwen2,3
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| 刊名 | SIAM JOURNAL ON IMAGING SCIENCES
 |
| 出版日期 | 2019 |
| 卷号 | 12期号:1页码:119-152 |
| 关键词 | inverse scattering locally rough surface Dirichlet boundary condition phaseless near-field data full far-field data |
| ISSN号 | 1936-4954 |
| DOI | 10.1137/18M1210204 |
| 英文摘要 | This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed frequency in two dimensions. We consider the case where a Dirichlet boundary condition is imposed on the locally rough surface. This problem models inverse scattering of plane acoustic waves by a one-dimensional sound-soft, locally rough surface; it also models inverse scattering of plane electromagnetic waves by a locally perturbed, perfectly reflecting, infinite plane in the transverse electric polarization case. We prove that the locally rough surface is uniquely determined by the phaseless near-field data generated by a countably infinite number of plane waves and measured on an open domain above the locally rough surface. Further, a direct imaging method is proposed to reconstruct the locally rough surface from the phaseless near-field data generated by plane waves and measured on the upper part of the circle with a sufficiently large radius. Theoretical analysis of the imaging algorithm is derived by making use of properties of the scattering solution and results from the theory of oscillatory integrals (especially the method of stationary phase). Moreover, as a by-product of the theoretical analysis, a similar direct imaging method with full far-field data is also proposed to reconstruct the locally rough surface. Finally, numerical experiments are carried out to demonstrate that the imaging algorithms with phaseless near-field data and full far-field data are fast, accurate, and very robust with respect to noise in the data. |
| 资助项目 | National Natural Science Foundation of China[91630309] ; National Natural Science Foundation of China[11501558] ; National Natural Science Foundation of China[11571355] ; National Natural Science Foundation of China[11871466] |
| WOS研究方向 | Computer Science ; Mathematics ; Imaging Science & Photographic Technology |
| 语种 | 英语 |
| WOS记录号 | WOS:000462628900005 |
| 出版者 | SIAM PUBLICATIONS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34263]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Xu, Xiaoxu |
| 作者单位 | 1.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.Chinese Acad Sci, NCMIS, Beijing 100190, Peoples R China 4.Chinese Acad Sci, LSEC, NCMIS, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Xiaoxu,Zhang, Bo,Zhang, Haiwen. Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data[J]. SIAM JOURNAL ON IMAGING SCIENCES,2019,12(1):119-152. |
| APA | Xu, Xiaoxu,Zhang, Bo,&Zhang, Haiwen.(2019).Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data.SIAM JOURNAL ON IMAGING SCIENCES,12(1),119-152. |
| MLA | Xu, Xiaoxu,et al."Uniqueness and Direct Imaging Method for Inverse Scattering by Locally Rough Surfaces with Phaseless Near-Field Data".SIAM JOURNAL ON IMAGING SCIENCES 12.1(2019):119-152. |
入库方式： OAI收割
来源：数学与系统科学研究院
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