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Title: Generalized proximal smoothing (GPS) for phase retrieval

Abstract

In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and support constraint. We relax the support constraint by incorporating the Moreau-Yosida regularization and heat kernel smoothing, and derive the associated proximal mapping. We also relax the magnitude constraint into a least squares fidelity term, whose proximal mapping is available as well. GPS alternatively iterates between the two proximal mappings in primal and dual spaces, respectively. Using both numerical simulation and experimental data, we show that GPS algorithm consistently outperforms the classical phase retrieval algorithms such as hybrid input-output (HIO) and oversampling smoothness (OSS), in terms of the convergence speed, consistency of the phase retrieval, and robustness to noise.

Authors:
ORCiD logo; ; ; ;
Publication Date:
Research Org.:
Univ. of California, Los Angeles, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1492877
Alternate Identifier(s):
OSTI ID: 1612034
Grant/Contract Number:  
SC0013838
Resource Type:
Published Article
Journal Name:
Optics Express
Additional Journal Information:
Journal Name: Optics Express Journal Volume: 27 Journal Issue: 3; Journal ID: ISSN 1094-4087
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Optics

Citation Formats

Pham, Minh, Yin, Penghang, Rana, Arjun, Osher, Stanley, and Miao, Jianwei. Generalized proximal smoothing (GPS) for phase retrieval. United States: N. p., 2019. Web. doi:10.1364/OE.27.002792.
Pham, Minh, Yin, Penghang, Rana, Arjun, Osher, Stanley, & Miao, Jianwei. Generalized proximal smoothing (GPS) for phase retrieval. United States. doi:https://doi.org/10.1364/OE.27.002792
Pham, Minh, Yin, Penghang, Rana, Arjun, Osher, Stanley, and Miao, Jianwei. Tue . "Generalized proximal smoothing (GPS) for phase retrieval". United States. doi:https://doi.org/10.1364/OE.27.002792.
@article{osti_1492877,
title = {Generalized proximal smoothing (GPS) for phase retrieval},
author = {Pham, Minh and Yin, Penghang and Rana, Arjun and Osher, Stanley and Miao, Jianwei},
abstractNote = {In this paper, we report the development of the generalized proximal smoothing (GPS) algorithm for phase retrieval of noisy data. GPS is a optimization-based algorithm, in which we relax both the Fourier magnitudes and support constraint. We relax the support constraint by incorporating the Moreau-Yosida regularization and heat kernel smoothing, and derive the associated proximal mapping. We also relax the magnitude constraint into a least squares fidelity term, whose proximal mapping is available as well. GPS alternatively iterates between the two proximal mappings in primal and dual spaces, respectively. Using both numerical simulation and experimental data, we show that GPS algorithm consistently outperforms the classical phase retrieval algorithms such as hybrid input-output (HIO) and oversampling smoothness (OSS), in terms of the convergence speed, consistency of the phase retrieval, and robustness to noise.},
doi = {10.1364/OE.27.002792},
journal = {Optics Express},
number = 3,
volume = 27,
place = {United States},
year = {2019},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: https://doi.org/10.1364/OE.27.002792

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