Almost everywhere injectivity conditions for the matrix recovery problem
文献类型：期刊论文
| 作者 | Rong, Yi3; Wang, Yang3; Xu, Zhiqiang1,2 |
| 刊名 | APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
 |
| 出版日期 | 2021 |
| 卷号 | 50页码:386-400 |
| 关键词 | Low-rank matrix recovery Determinant variety Rank minimization Compressed sensing |
| ISSN号 | 1063-5203 |
| DOI | 10.1016/j.acha.2019.09.002 |
| 英文摘要 | The aim of matrix recovery is to recover P is an element of M subset of F-pxq from L-A (P) = (Tr(A(1)(T)P), Tr(A(2)(T)P), ..., Tr(A(N)(T)P))(T) with A(j) is an element of V-j subset of F-pxq, which is raised in many areas. In this paper, we build up a framework for almost everywhere matrix recovery which means L-A is almost everywhere injectivity on M. We mainly focus on the following question: how many measurements are needed to recover almost all the matrices in M? For the case where both M and V-j are algebraic varieties, we use the tools from algebraic geometry to study the question and present some results to address it under many different settings. (C) 2019 Elsevier Inc. All rights reserved. |
| 资助项目 | NSFC[91630203] ; NSFC[11688101] ; Hong Kong Research Grant Council[16306415] ; Hong Kong Research Grant Council[16317416] ; Beijing Natural Science Foundation[Z180002] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000579922900013 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/52343]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Xu, Zhiqiang |
| 作者单位 | 1.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China |
| 推荐引用方式 GB/T 7714 | Rong, Yi,Wang, Yang,Xu, Zhiqiang. Almost everywhere injectivity conditions for the matrix recovery problem[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2021,50:386-400. |
| APA | Rong, Yi,Wang, Yang,&Xu, Zhiqiang.(2021).Almost everywhere injectivity conditions for the matrix recovery problem.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,50,386-400. |
| MLA | Rong, Yi,et al."Almost everywhere injectivity conditions for the matrix recovery problem".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 50(2021):386-400. |
入库方式： OAI收割
来源：数学与系统科学研究院
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