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On Robust Phase Retrieval for Sparse Signals

Jaganathan, Kishore and Oymak, Samet and Hassibi, Babak (2012) On Robust Phase Retrieval for Sparse Signals. In: 2012 50th Annual Allerton Conference on Communication, Control, and Computing. IEEE , Piscataway, NJ, pp. 794-799. ISBN 978-1-4673-4537-8.

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Recovering signals from their Fourier transform magnitudes is a classical problem referred to as phase retrieval and has been around for decades. In general, the Fourier transform magnitudes do not carry enough information to uniquely identify the signal and therefore additional prior information is required. In this paper, we shall assume that the underlying signal is sparse, which is true in many applications such as X-ray crystallography, astronomical imaging, etc. Recently, several techniques involving semidefinite relaxations have been proposed for this problem, however very little analysis has been performed. The phase retrieval problem can be decomposed into two tasks - (i) identifying the support of the sparse signal from the Fourier transform magnitudes, and (ii) recovering the signal using the support information. In earlier work [13], we developed algorithms for (i) which provably recovered the support for sparsities upto O(n^(1/3-ϵ)). Simulations suggest that support recovery is possible upto sparsity O(n^(1/2-ϵ)). In this paper, we focus on (ii) and propose an algorithm based on semidefinite relaxation, which provably recovers the signal from its Fourier transform magnitude and support knowledge with high probability if the support size is O(n^(1/2-ϵ)).

Item Type:Book Section
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Jaganathan, Kishore0000-0002-7829-4892
Additional Information:© 2012 IEEE. U.S. Government work not protected by U.S. copyright. 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) Multidisciplinary University Research Initiative (MURI)N00014-08-1-0747
Caltech Lee Center for Advanced NetworkingUNSPECIFIED
Subject Keywords:Phase Retrieval, Semidefinite Relaxation, Sparse Signals, Autocorrelation
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INSPEC Accession Number13400717
Record Number:CaltechAUTHORS:20130730-135255859
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Official Citation:Jaganathan, K.; Oymak, S.; Hassibi, B., "On robust phase retrieval for sparse signals," Communication, Control, and Computing (Allerton), 2012 50th Annual Allerton Conference on , vol., no., pp.794,799, 1-5 Oct. 2012 doi: 10.1109/Allerton.2012.6483299
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:39660
Deposited By: Ruth Sustaita
Deposited On:30 Jul 2013 21:30
Last Modified:09 Mar 2020 13:18

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