The recovery of complex sparse signals from few phaseless measurements

doi:10.1016/j.acha.2020.08.001

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	The recovery of complex sparse signals from few phaseless measurements
	Xia, Yu 1; Xu, Zhiqiang 2,3
	2021
发表期刊	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
ISSN	1063-5203
卷号	50 页码:1-15
摘要	We study the stable recovery of complex k-sparse signals from as few phaseless measurements as possible. The main result is to show that one can employ Li minimization to stably recover complex k-sparse signals from m >= O(k log(n/k)) complex Gaussian random quadratic measurements with high probability. To do that, we establish that Gaussian random measurements satisfy the restricted isometry property over rank-2 and sparse matrices with high probability. This paper presents the first theoretical estimation of the measurement number for stably recovering complex sparse signals from complex Gaussian quadratic measurements. (C) 2020 Elsevier Inc. All rights reserved.
DOI	10.1016/j.acha.2020.08.001
收录类别	SCI
语种	英语
资助项目	NSFC[11688101] ; NSFC[11901143] ; Zhejiang Provincial Natural Science Foundation[LQ19A010008] ; Department of Education of Zhejiang ProvinceScience Foundation[Y201840082] ; Beijing Natural Science Foundation[Z180002]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000579922900001
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/52356
专题	中国科学院数学与系统科学研究院
通讯作者	Xia, Yu
作者单位	1.Hangzhou Normal Univ, Dept Math, Hangzhou 311121, 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	Xia, Yu,Xu, Zhiqiang. The recovery of complex sparse signals from few phaseless measurements[J]. APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,2021,50:1-15.
APA	Xia, Yu,&Xu, Zhiqiang.(2021).The recovery of complex sparse signals from few phaseless measurements.APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS,50,1-15.
MLA	Xia, Yu,et al."The recovery of complex sparse signals from few phaseless measurements".APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS 50(2021):1-15.