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The l(1)-Analysis in Phase Retrieval with Redundant Dictionary
Gao, Bing
2017-10-01
Source PublicationJOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
ISSN1069-5869
Volume23Issue:5Pages:1097-1117
AbstractThis 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.
KeywordCompressed sensing Phase retrieval Sparse recovery l(1)-analysis
DOI10.1007/s00041-016-9500-z
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000411937600005
PublisherSPRINGER BIRKHAUSER
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26724
Collection中国科学院数学与系统科学研究院
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100091, Peoples R China
Recommended Citation
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.
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