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A Smoothing Stochastic Phase Retrieval Algorithm for Solving Random Quadratic Systems

Pinilla, Samuel and Bacca, Jorge and Tourneret, Jean-Yves and Arguello, Henry A Smoothing Stochastic Phase Retrieval Algorithm for Solving Random Quadratic Systems. (2018) In: IEEE Statistical Signal Processing Workshop (SSP 2018), 10 June 2018 - 13 June 2018 (Freiburg, Germany).

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Official URL: https://doi.org/10.1109/SSP.2018.8450729

Abstract

A novel Stochastic Smoothing Phase Retrieval (SSPR) algorithm is studied to reconstruct an unknown signal x ¿ ¿ n or Cn from a set of absolute square projections y k = |¿a k ; x¿| 2 . This inverse problem is known in the literature as Phase Retrieval (PR). Recent works have shown that the PR problem can be solved by optimizing a nonconvex and non-smooth cost function. Contrary to the recent truncated gradient descend methods developed to solve the PR problem (using truncation parameters to bypass the non-smoothness of the cost function), the proposed algorithm approximates the cost function of interest by a smooth function. Optimizing this smooth function involves a single equation per iteration, which leads to a simple scalable and fast method especially for large sample sizes. Extensive simulations suggest that SSPR requires a reduced number of measurements for recovering the signal x, when compared to recently developed stochastic algorithms. Our experiments also demonstrate that SSPR is robust to the presence of additive noise and has a speed of convergence comparable with that of state-of-the-art algorithms.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to IEEE editor. The definitive version is available at http://ieeexplore.ieee.org This papers appears in Proceedings of SSP 2018. ISBN: 978-1-5386-1571-3 The original PDF of the article can be found at: Electronic https://ieeexplore.ieee.org/document/8450729 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.
HAL Id:hal-02494105
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - Toulouse INP (FRANCE)
Other partners > Universidad Industrial de Santander - UIS (COLOMBIA)
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)
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Deposited On:19 Feb 2020 08:25

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