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Sparse Phase Retrieval: Convex Algorithms and Limitations

Jaganathan, Kishore and Oymak, Samet and Hassibi, Babak (2013) Sparse Phase Retrieval: Convex Algorithms and Limitations. In: 2013 IEEE International Symposium on Information Theory Proceedings (ISIT),. IEEE , Piscataway, NJ, pp. 1022-1026. https://resolver.caltech.edu/CaltechAUTHORS:20150126-071647266

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Abstract

We consider the problem of recovering signals from their power spectral densities. This is a classical problem referred to in literature as the phase retrieval problem, and is of paramount importance in many fields of applied sciences. In general, additional prior information about the signal is required to guarantee unique recovery as the mapping from signals to power spectral densities is not one-to-one. In this work, we assume that the underlying signals are sparse. Recently, semidefinite programming (SDP) based approaches were explored by various researchers. Simulations of these algorithms strongly suggest that signals upto O(n^(1/2−ϵ) sparsity can be recovered by this technique. In this work, we develop a tractable algorithm based on reweighted ℓ_1-minimization that recovers a sparse signal from its power spectral density for significantly higher sparsities, which is unprecedented. We also discuss the limitations of the existing SDP algorithms and provide a combinatorial algorithm which requires significantly fewer ”phaseless” measurements to guarantee recovery.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2013.6620381DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6620381PublisherArticle
http://arxiv.org/abs/1303.4128arXivDiscussion Paper
ORCID:
AuthorORCID
Jaganathan, Kishore0000-0002-7829-4892
Additional Information:© 2013 IEEE. This work was supported in part by the National Science Foundation under grants CCF-0729203, CNS-0932428 and CCF-1018927, by the Office of Naval Research under the MURI grant N00014-08-1-0747, and by Caltech’s Lee Center for Advanced Networking.
Funders:
Funding AgencyGrant Number
NSFCCF-0729203
NSFCNS-0932428
NSFCCF-1018927
Office of Naval Research (ONR)N00014-08-1-0747
Caltech’s Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Phase Retrieval, Phaseless measurements, Semidefinite Programming (SDP), Reweighted ℓ_1-minimization
Record Number:CaltechAUTHORS:20150126-071647266
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150126-071647266
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:54045
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:26 Jan 2015 21:42
Last Modified:09 Mar 2020 13:18

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