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On Fienup Methods for Sparse Phase Retrieval

Pauwels, Edouard and Beck, Amir and Yonina C., Eldar and Sabach, Shoham On Fienup Methods for Sparse Phase Retrieval. (2017) IEEE Transactions on Signal Processing, 66 (4). 982-991. ISSN 1053-587X

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Official URL: https://doi.org/10.1109/TSP.2017.2780044

Abstract

Alternating minimization, or Fienup methods, have a long history in phase retrieval. We provide new insights related to the empirical and theoretical analysis of these algorithms when used with Fourier measurements and combined with convex priors. In particular, we show that Fienup methods can be viewed as performing alternating minimization on a regularized nonconvex least-squares problem with respect to amplitude measurements. Furthermore, we prove that under mild additional structural assumptions on the prior (semialgebraicity), the sequence of signal estimates has a smooth convergent behavior toward a critical point of the nonconvex regularized least-squares objective. Finally, we propose an extension to Fienup techniques, based on a projected gradient descent interpretation and acceleration using inertial terms. We demonstrate experimentally that this modification combined with an ℓ 1 prior constitutes a competitive approach for sparse phase retrieval.

Item Type:Article
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org The original PDF can be found at IEEE Transactions on Signal Processing (ISSN 1053-587X) website : https://ieeexplore.ieee.org/document/8141921 Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Other partners > University of Haifa (ISRAEL)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UT3 (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Tel Aviv University (ISRAEL)
Laboratory name:
Funders:
AFRL: Air Force Research Laboratory, Air Force Office of Scientific Research (US) - Israel Science Foundation (Israël)
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Deposited On:11 Oct 2019 14:24

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