The l(1)-Analysis in Phase Retrieval with Redundant Dictionary

doi:10.1007/s00041-016-9500-z

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	The l(1)-Analysis in Phase Retrieval with Redundant Dictionary
	Gao, Bing
	2017-10-01
发表期刊	JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
ISSN	1069-5869
卷号	23 期号:5 页码:1097-1117
摘要	This article presents new results concerning the recovery of a signal from the magnitude only measurements where the signal is not sparse in an orthonormal basis but in a redundant dictionary, which we call it phase retrieval with redundant dictionary for short. To solve this phaseless problem, we analyze the -analysis model. Firstly we investigate the noiseless case with presenting a null space property of the measurement matrix under which the -analysis model provides an exact recovery. Secondly we introduce a new property (S-DRIP) of the measurement matrix. By solving the -analysis model, we prove that this property can guarantee a stable recovery of real signals that are nearly sparse in overcomplete dictionaries.
关键词	Compressed sensing Phase retrieval Sparse recovery l(1)-analysis
DOI	10.1007/s00041-016-9500-z
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000411937600005
出版者	SPRINGER BIRKHAUSER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26724
专题	中国科学院数学与系统科学研究院
通讯作者	Gao, Bing
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100091, Peoples R China
推荐引用方式 GB/T 7714	Gao, Bing. The l(1)-Analysis in Phase Retrieval with Redundant Dictionary[J]. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,2017,23(5):1097-1117.
APA	Gao, Bing.(2017).The l(1)-Analysis in Phase Retrieval with Redundant Dictionary.JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS,23(5),1097-1117.
MLA	Gao, Bing."The l(1)-Analysis in Phase Retrieval with Redundant Dictionary".JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS 23.5(2017):1097-1117.