Phase retrieval from the norms of affine transformations
文献类型：期刊论文
| 作者 | Huang, Meng2; Xu, Zhiqiang1,2 |
| 刊名 | ADVANCES IN APPLIED MATHEMATICS
 |
| 出版日期 | 2021-09-01 |
| 卷号 | 130页码:20 |
| 关键词 | Phase retrieval Determinant variety Matrix recovery |
| ISSN号 | 0196-8858 |
| DOI | 10.1016/j.aam.2021.102213 |
| 英文摘要 | In this paper, we consider the generalized phase retrieval from affine measurements. This problem aims to recover signals x is an element of F-d from the magnitude of the affine transformations y(j) = parallel to M-j* x + b(j) parallel to + 1 )(2)(2) j = 1, ..., m, where M-j is an element of F-dxr, b(j) is an element of F-r, F is an element of {R, C} and we call it generalized affine phase retrieval. We first develop a framework for generalized affine phase retrieval with presenting several necessary and sufficient conditions for {(M-j, b(j))}(j=1)(m) having generalized affine phase retrieval property. Next, we focus on the minimal measurement number problem and establish some results for it. Particularly, we show if {(M-j, b(j))}(j=1)(m), subset of F-dxr x F-r has generalized affine phase retrieval property, then m >= d+ left perpendiculard/rright perpendicular for F = R (m >= 2d+ left perpendiculard/rright perpendicular for F = C). We also show that the lower bounds are tight provided r vertical bar d. These results imply that one can reduce the measurement number by raising r, i.e. the rank of M-j. This highlights a notable difference between generalized affine phase retrieval and generalized phase retrieval. Furthermore, using tools of algebraic geometry, we show that m >= 2d (resp. m >= 4d-1) generic measurements A = {(M-j, b(j))}(j=1)(m) have the generalized phase retrieval property for F = R (resp. F = C). (C) 2021 Elsevier Inc. All rights reserved. |
| 资助项目 | National Science Fund for Distinguished Young Scholars grant[12025108] ; Beijing Natural Science Foundation[Z180002] ; NSFC[12021001] ; NSFC[11688101] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000680040300009 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/58990]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Huang, Meng |
| 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, Inst Comp Math, LSEC, Beijing 100091, Peoples R China |
| 推荐引用方式 GB/T 7714 | Huang, Meng,Xu, Zhiqiang. Phase retrieval from the norms of affine transformations[J]. ADVANCES IN APPLIED MATHEMATICS,2021,130:20. |
| APA | Huang, Meng,&Xu, Zhiqiang.(2021).Phase retrieval from the norms of affine transformations.ADVANCES IN APPLIED MATHEMATICS,130,20. |
| MLA | Huang, Meng,et al."Phase retrieval from the norms of affine transformations".ADVANCES IN APPLIED MATHEMATICS 130(2021):20. |
入库方式： OAI收割
来源：数学与系统科学研究院
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