The minimal measurement number for low-rank matrix recovery
文献类型：期刊论文
| 作者 | Xu, Zhiqiang
|
| 刊名 | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
 |
| 出版日期 | 2018-03-01 |
| 卷号 | 44期号:2页码:497-508 |
| 关键词 | Low-rank matrices Phase retrieval Determinant variety |
| ISSN号 | 1063-5203 |
| DOI | 10.1016/j.acha.2017.01.005 |
| 英文摘要 | The paper presents several results that address a fundamental question in low-rank matrix recovery: how many measurements are needed to recover low-rank matrices? We begin by investigating the complex matrices case and show that 4nr - 4r(2) generic measurements are both necessary and sufficient for the recovery of rank-r matrices in C-nxn. Thus, we confirm a conjecture which is raised by Eldar, Needell and Plan for the complex case. We next consider the real case and prove that the bound 4nr - 4r(2) is tight provided n = 2(k) + r, k is an element of Z(+) Motivated by Vinzant's work [19], we construct 11 matrices in R-4 X 4 by computer random search and prove they define injective measurements on rank-1 matrices in R-4x4. This disproves the conjecture raised by Eldar, Needell and Plan for the real case. Finally, we use the results in this paper to investigate the phase retrieval by projection and show fewer than 2n - 1 orthogonal projections are possible for the recovery of x is an element of R-n from the norm of them, which gives a negative answer for a question raised in [1]. (C) 2017 Elsevier Inc. All rights reserved. |
| 语种 | 英语 |
| WOS记录号 | WOS:000423781300011 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/29543]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Xu, Zhiqiang |
| 作者单位 | Chinese Acad Sci, Acad Math & Syst Sci, LSEC, Inst Comp Math, Beijing 100091, Peoples R China |
| 推荐引用方式 GB/T 7714 | Xu, Zhiqiang. The minimal measurement number for low-rank matrix recovery[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2018,44(2):497-508. |
| APA | Xu, Zhiqiang.(2018).The minimal measurement number for low-rank matrix recovery.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,44(2),497-508. |
| MLA | Xu, Zhiqiang."The minimal measurement number for low-rank matrix recovery".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 44.2(2018):497-508. |
入库方式： OAI收割
来源：数学与系统科学研究院
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