Almost everywhere injectivity conditions for the matrix recovery problem

doi:10.1016/j.acha.2019.09.002

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	Almost everywhere injectivity conditions for the matrix recovery problem
	Rong, Yi 1; Wang, Yang 1; Xu, Zhiqiang 2,3
	2021
发表期刊	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
ISSN	1063-5203
卷号	50 页码:386-400
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.
关键词	Low-rank matrix recovery Determinant variety Rank minimization Compressed sensing
DOI	10.1016/j.acha.2019.09.002
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000579922900013
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52344
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.Hong Kong Univ Sci & Technol, Dept Math, Kowloon, Clear Water Bay, Hong Kong, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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.