Phaseless Recovery Using the Gauss-Newton Method

doi:10.1109/TSP.2017.2742981

	Phaseless Recovery Using the Gauss-Newton Method
	Gao, Bing; Xu, Zhiqiang
	2017-11-15
发表期刊	IEEE TRANSACTIONS ON SIGNAL PROCESSING
ISSN	1053-587X
卷号	65 期号:22 页码:5885-5896
摘要	In 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.
关键词	Phaseless recovery phase retrieval Gauss-Newton method quadratic convergence
DOI	10.1109/TSP.2017.2742981
语种	英语
资助项目	NSFC[11422113] ; NSFC[91630203] ; NSFC[11331012] ; National Basic Research Program of China (973 Program)[2015CB856000]
WOS研究方向	Engineering
WOS类目	Engineering, Electrical & Electronic
WOS记录号	WOS:000411680100005
出版者	IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/26641
专题	计算数学与科学工程计算研究所
通讯作者	Xu, Zhiqiang
作者单位	Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100864, Peoples R China
推荐引用方式 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.