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Phaseless Recovery Using the Gauss-Newton Method
Gao, Bing; Xu, Zhiqiang
2017-11-15
Source PublicationIEEE TRANSACTIONS ON SIGNAL PROCESSING
ISSN1053-587X
Volume65Issue:22Pages:5885-5896
AbstractIn this paper, we propose a Gauss-Newton algorithm to recover an n-dimensional signal from its phaseless measurements. The algorithm has two stages. In the first stage, the algorithm obtains a good initialization by calculating the eigenvector corresponding to the largest eigenvalue of a Hermitian matrix. In the second stage, the algorithm solves an optimization problem iteratively using the Gauss-Newton method. Our initialization method makes full use of all measurements and provides a good initial guess, as long as the number of random measurements is O(n). For real-valued signals, we prove that a resampled version of Gauss-Newton iterations converges to the global optimal solution quadratically with O(n log n) random measurements. Numerical experiments show that the Gauss-Newton method has better empirical performance than other algorithms, such as the Wirtinger flow algorithm and Altmin phase algorithm.
KeywordPhaseless recovery phase retrieval Gauss-Newton method quadratic convergence
DOI10.1109/TSP.2017.2742981
Language英语
Funding ProjectNSFC[11422113] ; NSFC[91630203] ; NSFC[11331012] ; National Basic Research Program of China (973 Program)[2015CB856000]
WOS Research AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000411680100005
PublisherIEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
Citation statistics
Cited Times:4[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/26641
Collection计算数学与科学工程计算研究所
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100864, Peoples R China
Recommended Citation
GB/T 7714
Gao, Bing,Xu, Zhiqiang. Phaseless Recovery Using the Gauss-Newton Method[J]. IEEE TRANSACTIONS ON SIGNAL PROCESSING,2017,65(22):5885-5896.
APA Gao, Bing,&Xu, Zhiqiang.(2017).Phaseless Recovery Using the Gauss-Newton Method.IEEE TRANSACTIONS ON SIGNAL PROCESSING,65(22),5885-5896.
MLA Gao, Bing,et al."Phaseless Recovery Using the Gauss-Newton Method".IEEE TRANSACTIONS ON SIGNAL PROCESSING 65.22(2017):5885-5896.
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