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Title: Ptychographic phase retrieval by proximal algorithms

Abstract

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 104 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.

Authors:
ORCiD logo [1]
  1. Brookhaven National Lab. (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)
Publication Date:
Research Org.:
Brookhaven National Laboratory (BNL), Upton, NY (United States). National Synchrotron Light Source II (NSLS-II)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1614980
Report Number(s):
BNL-213843-2020-JAAM
Journal ID: ISSN 1367-2630
Grant/Contract Number:  
SC0012704
Resource Type:
Accepted Manuscript
Journal Name:
New Journal of Physics
Additional Journal Information:
Journal Volume: 22; Journal Issue: 2; Journal ID: ISSN 1367-2630
Publisher:
IOP Publishing
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ptychographic phase-retrieval; proximal algorithms; x-ray imaging; maximum-likelihood

Citation Formats

Yan, Hanfei. Ptychographic phase retrieval by proximal algorithms. United States: N. p., 2020. Web. doi:10.1088/1367-2630/ab704e.
Yan, Hanfei. Ptychographic phase retrieval by proximal algorithms. United States. doi:https://doi.org/10.1088/1367-2630/ab704e
Yan, Hanfei. Wed . "Ptychographic phase retrieval by proximal algorithms". United States. doi:https://doi.org/10.1088/1367-2630/ab704e. https://www.osti.gov/servlets/purl/1614980.
@article{osti_1614980,
title = {Ptychographic phase retrieval by proximal algorithms},
author = {Yan, Hanfei},
abstractNote = {We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 104 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.},
doi = {10.1088/1367-2630/ab704e},
journal = {New Journal of Physics},
number = 2,
volume = 22,
place = {United States},
year = {2020},
month = {2}
}

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