The recovery of complex sparse signals from few phaseless measurements

doi:10.1016/j.acha.2020.08.001

	The recovery of complex sparse signals from few phaseless measurements
	Xia, Yu 1; Xu, Zhiqiang 2,3
刊名	APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
	2021
卷号	50 页码:1-15
ISSN号	1063-5203
DOI	10.1016/j.acha.2020.08.001
英文摘要	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.
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
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000579922900001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52355]
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.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Comp Math, LSEC, Beijing 100091, 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.