NDLI: Phase retrieval with masks using convex optimization

Content Provider	IEEE Xplore Digital Library
Author	Jaganathan, K. Eldar, Y. Hassibi, B.
Copyright Year	2015
Description	Author affiliation: Dept. of Electr. Eng., Caltech, Pasadena, CA, USA (Jaganathan, K.; Hassibi, B.) \|\| Dept. of Electr. Eng., Technion - Israel Inst. of Technol., Haifa, Israel (Eldar, Y.)
Abstract	Signal recovery from the magnitude of the Fourier transform, or equivalently, from the autocorrelation, is a classical problem known as phase retrieval. Due to the absence of phase information, some form of additional information is required in order to be able to uniquely identify the underlying signal. In this work, we consider the problem of phase retrieval using masks. Due to our interest in developing robust algorithms with theoretical guarantees, we explore a convex optimization-based framework. In this work, we show that two specific masks (each mask provides 2n Fourier magnitude measurements) or five specific masks (each mask provides n Fourier magnitude measurements) are sufficient for a convex relaxation of the phase retrieval problem to provably recover almost all signals (up to global phase). We also show that the recovery is stable in the presence of measurement noise. This is a significant improvement over the existing results, which require $O(log^{2}$ n) random masks (each mask provides n Fourier magnitude measurements) in order to guarantee unique recovery (up to global phase). Numerical experiments complement our theoretical analysis and show interesting trends, which we hope to explain in a future publication.
Starting Page	1655
Ending Page	1659
File Size	273730
Page Count	5
File Format	PDF
ISSN	21578117
e-ISBN	9781467377041
DOI	10.1109/ISIT.2015.7282737
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2015-06-14
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Noise measurement Phase measurement Fourier transforms Correlation Extraterrestrial measurements Noise Pollution measurement convex optimization phase retrieval masked signals autocorrelation semidefinite programming
Content Type	Text
Resource Type	Article

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

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