NDLI: Phase Retrieval Using Alternating Minimization

Content Provider	IEEE Xplore Digital Library
Author	Netrapalli, P. Jain, P. Sanghavi, S.
Copyright Year	1991
Abstract	Phase retrieval problems involve solving linear equations, but with missing sign (or phase, for complex numbers) information. More than four decades after it was first proposed, the seminal error reduction algorithm of Gerchberg and Saxton and Fienup is still the popular choice for solving many variants of this problem. The algorithm is based on alternating minimization; i.e., it alternates between estimating the missing phase information, and the candidate solution. Despite its wide usage in practice, no global convergence guarantees for this algorithm are known. In this paper, we show that a (resampling) variant of this approach converges geometrically to the solution of one such problem-finding a vector x from y, A, where y = \|A^Tx\| and \|z\| denotes a vector of element-wise magnitudes of z-under the assumption that A is Gaussian. Empirically, we demonstrate that alternating minimization performs similar to recently proposed convex techniques for this problem (which are based on “lifting” to a convex matrix problem) in sample complexity and robustness to noise. However, it is much more efficient and can scale to large problems. Analytically, for a resampling version of alternating minimization, we show geometric convergence to the solution, and sample complexity that is off by log factors from obvious lower bounds. We also establish close to optimal scaling for the case when the unknown vector is sparse. Our work represents the first theoretical guarantee for alternating minimization (albeit with resampling) for any variant of phase retrieval problems in the non-convex setting.
Sponsorship	IEEE Signal Processing Society
Starting Page	4814
Ending Page	4826
Page Count	13
File Size	2811389
File Format	PDF
ISSN	1053587X
Volume Number	63
Issue Number	18
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-01-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Signal processing algorithms Minimization Phase measurement Convergence Algorithm design and analysis Complexity theory Electronic mail optics Phase retrieval alternating minimization crystallography
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Linear Beamformer Design for Interference Alignment via Rank Minimization

Space-alternating generalized expectation-maximization algorithm

Fast algorithms for subspace tracking

Improved Newton-type algorithm for adaptive implementation of Pisarenko's harmonic retrieval method and its convergence analysis

Locally optimum adaptive signal processing algorithms

DOA Estimation Using a Greedy Block Coordinate Descent Algorithm

Robust broadband periodic excitation design

Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization and Shrinkage

Can one evaluate the Gabor expansion using Gabor's iterative algorithm?

Phase Retrieval Using Alternating Minimization

Similar Documents

Linear Beamformer Design for Interference Alignment via Rank Minimization

Space-alternating generalized expectation-maximization algorithm

Fast algorithms for subspace tracking

Improved Newton-type algorithm for adaptive implementation of Pisarenko's harmonic retrieval method and its convergence analysis

Locally optimum adaptive signal processing algorithms

DOA Estimation Using a Greedy Block Coordinate Descent Algorithm

Robust broadband periodic excitation design

Sparsity-Aware Adaptive Algorithms Based on Alternating Optimization and Shrinkage

Can one evaluate the Gabor expansion using Gabor's iterative algorithm?

Phase Retrieval Using Alternating Minimization