Almost everywhere injectivity conditions for the matrix recovery problem

doi:10.1016/j.acha.2019.09.002

	Almost everywhere injectivity conditions for the matrix recovery problem
	Rong, Yi 3; Wang, Yang 3; Xu, Zhiqiang 1,2
刊名	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
	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
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000579922900013
内容类型	期刊论文
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.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 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.