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Title: Denoising Poisson phaseless measurements via orthogonal dictionary learning

Abstract

Phaseless diffraction measurements recorded by CCD detectors are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity in order to denoise such Poisson phaseless measurements. The model consists of three terms: (i) A representation term by an orthogonal dictionary, (ii) an L 0 pseudo norm of the coefficient matrix, and (iii) a Kullback-Leibler divergence term to fit phaseless Poisson data. Fast alternating minimization method (AMM) and proximal alternating linearized minimization (PALM) are adopted to solve the proposed model, and especially the theoretical guarantee of the convergence of PALM is provided. The subproblems for these two algorithms both have fast solvers, and indeed, the solutions for the sparse coding and dictionary updating both have closed forms due to the orthogonality of learned dictionaries. Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are conducted to show the efficiency and robustness of proposed methods, which, by preserving texture features, produce visually and quantitatively improved restored images compared with other phase retrieval algorithms without regularization and local sparsity promoting algorithms.

Authors:
 [1];  [2]
  1. Tianjin Normal Univ., Tianjin (China). School of Mathematical Sciences; Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
  2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Division
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); National Natural Science Foundation of China (NNSFC); Natural Science Foundation of Tianjin; China Scholarship Council; Tianjin Normal University
OSTI Identifier:
1506342
Grant/Contract Number:  
AC02-05CH11231; AC03-76SF00098
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Optics Express
Additional Journal Information:
Journal Volume: 26; Journal Issue: 16; Journal ID: ISSN 1094-4087
Publisher:
Optical Society of America (OSA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Chang, Huibin, and Marchesini, Stefano. Denoising Poisson phaseless measurements via orthogonal dictionary learning. United States: N. p., 2018. Web. doi:10.1364/OE.26.019773.
Chang, Huibin, & Marchesini, Stefano. Denoising Poisson phaseless measurements via orthogonal dictionary learning. United States. doi:10.1364/OE.26.019773.
Chang, Huibin, and Marchesini, Stefano. Mon . "Denoising Poisson phaseless measurements via orthogonal dictionary learning". United States. doi:10.1364/OE.26.019773. https://www.osti.gov/servlets/purl/1506342.
@article{osti_1506342,
title = {Denoising Poisson phaseless measurements via orthogonal dictionary learning},
author = {Chang, Huibin and Marchesini, Stefano},
abstractNote = {Phaseless diffraction measurements recorded by CCD detectors are often affected by Poisson noise. In this paper, we propose a dictionary learning model by employing patches based sparsity in order to denoise such Poisson phaseless measurements. The model consists of three terms: (i) A representation term by an orthogonal dictionary, (ii) an L0 pseudo norm of the coefficient matrix, and (iii) a Kullback-Leibler divergence term to fit phaseless Poisson data. Fast alternating minimization method (AMM) and proximal alternating linearized minimization (PALM) are adopted to solve the proposed model, and especially the theoretical guarantee of the convergence of PALM is provided. The subproblems for these two algorithms both have fast solvers, and indeed, the solutions for the sparse coding and dictionary updating both have closed forms due to the orthogonality of learned dictionaries. Numerical experiments for phase retrieval using coded diffraction and ptychographic patterns are conducted to show the efficiency and robustness of proposed methods, which, by preserving texture features, produce visually and quantitatively improved restored images compared with other phase retrieval algorithms without regularization and local sparsity promoting algorithms.},
doi = {10.1364/OE.26.019773},
journal = {Optics Express},
issn = {1094-4087},
number = 16,
volume = 26,
place = {United States},
year = {2018},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 1 work
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Figures / Tables:

Fig. 1. Fig. 1.: Ground truth images. Real-valued images of resolution 512 512 in (a): Peppers; (b): Fingerprint; (c): Barbara; (d): House; A complex-valued image “Goldballs” of resolution 256 256 with magnitude, real and imaginary parts in (e), (f) and (g), respectively.

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Works referencing / citing this record:

Advanced denoising for X-ray ptychography
journal, January 2019

  • Chang, Huibin; Enfedaque, Pablo; Zhang, Jie
  • Optics Express, Vol. 27, Issue 8
  • DOI: 10.1364/oe.27.010395