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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.

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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
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URLURL TypeDescription DOIArticle Paper
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.
Funding AgencyGrant Number
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
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INSPEC Accession Number12962892
Series Name:IEEE International Symposium on Information Theory
Record Number:CaltechAUTHORS:20130204-114142719
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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
Deposited By: Jason Perez
Deposited On:04 Feb 2013 21:48
Last Modified:09 Mar 2020 13:18

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