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Recovery of sparse 1-D signals from the magnitudes of their Fourier transform

Jaganathan, Kishore and Oymak, Samet and Hassibi, Babak (2012) Recovery of sparse 1-D signals from the magnitudes of their Fourier transform. In: 2012 IEEE International Symposium on Information Theory Proceedings. IEEE International Symposium on Information Theory. IEEE , Piscataway, NJ, pp. 1473-1477. ISBN 978-1-4673-2580-6. https://resolver.caltech.edu/CaltechAUTHORS:20130204-114142719

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Abstract

The problem of signal recovery from the autocorrelation, or equivalently, the magnitudes of the Fourier transform, is of paramount importance in various fields of engineering. In this work, for one-dimensional signals, we give conditions, which when satisfied, allow unique recovery from the autocorrelation with very high probability. In particular, for sparse signals, we develop two non-iterative recovery algorithms. One of them is based on combinatorial analysis, which we prove can recover signals up to sparsity o(n^(1/3)) with very high probability, and the other is developed using a convex optimization based framework, which numerical simulations suggest can recover signals upto sparsity o(n^(1/2)) with very high probability.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/ISIT.2012.6283508 DOIArticle
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6283508PublisherArticle
http://arxiv.org/abs/1206.1405v1arXivDiscussion Paper
ORCID:
AuthorORCID
Jaganathan, Kishore0000-0002-7829-4892
Additional Information:© 2012 IEEE. Date of Conference: 1-6 July 2012; Date of Current Version: 27 August 2012. 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) MURIN00014-08-1-0747
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Autocorrelation; Phase Retrieval; Convex Optimization; Sparse Spectral Factorization
Other Numbering System:
Other Numbering System NameOther Numbering System ID
INSPEC Accession Number12962892
Series Name:IEEE International Symposium on Information Theory
Record Number:CaltechAUTHORS:20130204-114142719
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20130204-114142719
Official Citation:Jaganathan, K.; Oymak, S.; Hassibi, B.; , "Recovery of sparse 1-D signals from the magnitudes of their Fourier transform," Information Theory Proceedings (ISIT), 2012 IEEE International Symposium on , vol., no., pp.1473-1477, 1-6 July 2012 doi: 10.1109/ISIT.2012.6283508
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:36759
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:04 Feb 2013 21:48
Last Modified:09 Mar 2020 13:18

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