Spectral Method for Phase Retrieval: An Expectation Propagation Perspective

doi:10.1109/TIT.2021.3049172

CSpace

	Spectral Method for Phase Retrieval: An Expectation Propagation Perspective
	Ma, Junjie 1,2,3; Dudeja, Rishabh 1; Xu, Ji 4; Maleki, Arian 1; Wang, Xiaodong 2
	2021-02-01
发表期刊	IEEE TRANSACTIONS ON INFORMATION THEORY
ISSN	0018-9448
卷号	67 期号:2 页码:1332-1355
摘要	Phase retrieval refers to the problem of recovering a signal x(star) is an element of C-n from its phaseless measurements y(i) = vertical bar a(i)(H) x(star)vertical bar, where {alpha(i)}(i=1)(m) are the measurement vectors. Spectral method is widely used for initialization in many phase retrieval algorithms. The quality of spectral initialization can have a major impact on the overall algorithm. In this paper, we focus on the model where A = [alpha(1), ... , alpha(m)](H) has orthonormal columns, and study the spectral initialization under the asymptotic setting m, n -> infinity with m/n infinity -> delta is an element of (1, infinity). We use the expectation propagation framework to characterize the performance of spectral initialization for Haar distributed matrices. Our numerical results confirm that the predictions of the EP method are accurate for not-only Haar distributed matrices, but also for realistic Fourier based models (e.g. the coded diffraction model). The main findings of this paper are the following: 1) There exists a threshold on delta(denoted as delta(weak)) below which the spectral method cannot produce a meaningful estimate. We show that delta(weak) = 2 for the column-orthonormal model. In contrast, previous results by Mondelli and Montanari show that delta(weak) = 1 for the i.i.d. Gaussian model. 2) The optimal design for the spectral method coincides with that for the i.i.d. Gaussian model, where the latter was recently introduced by Luo, Alghamdi and Lu.
关键词	Phase measurement Message passing Tools Signal processing algorithms Prediction algorithms Numerical models Approximation algorithms Phase retrieval spectral method coded diffraction pattern expectation propagation (EP) approximate message passing (AMP) state evolution orthogonal AMP vector AMP
DOI	10.1109/TIT.2021.3049172
收录类别	SCI
语种	英语
资助项目	National Science Foundation (NSF)[CCF 1814803] ; Office of Naval Research (ONR)[N000141712827]
WOS研究方向	Computer Science ; Engineering
WOS类目	Computer Science, Information Systems ; Engineering, Electrical & Electronic
WOS记录号	WOS:000612137400036
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/58192
专题	中国科学院数学与系统科学研究院
通讯作者	Ma, Junjie
作者单位	1.Columbia Univ, Dept Stat, New York, NY 10027 USA 2.Columbia Univ, Dept Elect Engn, New York, NY 10027 USA 3.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Acad Math & Syst Sci, Beijing 100190, Peoples R China 4.Columbia Univ, Dept Comp Sci, New York, NY 10027 USA
推荐引用方式 GB/T 7714	Ma, Junjie,Dudeja, Rishabh,Xu, Ji,et al. Spectral Method for Phase Retrieval: An Expectation Propagation Perspective[J]. IEEE TRANSACTIONS ON INFORMATION THEORY,2021,67(2):1332-1355.
APA	Ma, Junjie,Dudeja, Rishabh,Xu, Ji,Maleki, Arian,&Wang, Xiaodong.(2021).Spectral Method for Phase Retrieval: An Expectation Propagation Perspective.IEEE TRANSACTIONS ON INFORMATION THEORY,67(2),1332-1355.
MLA	Ma, Junjie,et al."Spectral Method for Phase Retrieval: An Expectation Propagation Perspective".IEEE TRANSACTIONS ON INFORMATION THEORY 67.2(2021):1332-1355.