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Title: Denoising Poisson phaseless measurements via orthogonal dictionary learning

Journal Article · · Optics Express
DOI:https://doi.org/10.1364/OE.26.019773· OSTI ID:1506342
 [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
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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.

Research Organization:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Natural Science Foundation of China (NSFC); Natural Science Foundation of Tianjin; China Scholarship Council; Tianjin Normal University
Grant/Contract Number:
AC02-05CH11231; AC03-76SF00098
OSTI ID:
1506342
Journal Information:
Optics Express, Vol. 26, Issue 16; ISSN 1094-4087
Publisher:
Optical Society of America (OSA)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

Cited By (1)

Advanced denoising for X-ray ptychography text January 2019

Figures / Tables (19)

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97 MATHEMATICS AND COMPUTING