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Blind Ptychographic Phase Retrieval via Convergent Alternating Direction Method of Multipliers

Huibin Chang, Pablo Enfedaque, Stefano Marchesini
2019 SIAM Journal of Imaging Sciences  
Next, we propose a generalized alternating direction method of multipliers designed for the proposed nonconvex models with convergence guarantee under mild conditions, where their subproblems can be solved  ...  A ptychographyic reconstruction is normally formulated as a blind phase retrieval problem, where both the image (sample) and the probe (illumination) have to be recovered from phaseless measured data.  ...  We would also like to thank Professor Wotao Yin in University of California, Los Angeles, for bringing to our attention some important references and further inspiring discussion. This  ... 
doi:10.1137/18m1188446 fatcat:5l77t36uubbxppilahkb7qn37y

A matrix-free Levenberg-Marquardt algorithm for efficient ptychographic phase retrieval [article]

Saugat Kandel, S. Maddali, Youssef S G Nashed, Stephan O Hruszkewycz, Chris Jacobsen, Marc Allain
2021 arXiv   pre-print
We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained "blind" ptychographic object and probe retrieval problems, under  ...  Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework.  ...  F.5 Alternating Directions Minimization The Alternating Directions Minimization (ADMM) method [86, 87] has recently been adapted as a provably convergent scheme for the BPR problem for both the magnitude-based  ... 
arXiv:2103.01767v1 fatcat:gfrt4jp4kbetvosp4lviygt7xi

Blind Ptychography by Douglas-Rachford Splitting [article]

A. Fannjiang, Z. Zhang
2018 arXiv   pre-print
Enhanced by the initialization method and the use of a randomly phased mask, AMDRS converges globally and geometrically.  ...  Based on alternating minimization by Douglas-Rachford splitting, AMDRS is a blind ptychographic algorithm informed by the uniqueness theory, the Poisson noise model and the stability analysis.  ...  Acknowledgements The research of A. F. is supported by the US National Science Foundation grant DMS-1413373.  ... 
arXiv:1809.00962v3 fatcat:eerga57p55e4zea2g47cfxadt4

Fixed Point Analysis of Douglas-Rachford Splitting for Ptychography and Phase Retrieval [article]

A. Fannjiang, Z. Zhang
2020 arXiv   pre-print
Douglas-Rachford Splitting (DRS) methods based on the proximal point algorithms for the Poisson and Gaussian log-likelihood functions are proposed for ptychography and phase retrieval.  ...  When applied to the challenging problem of blind ptychography, which seeks to recover both the object and the probe simultaneously, Alternating Minimization with the DRS inner loops, even with a far from  ...  The DRS method is an optimization method based on proximal operators, a natural extension of projections, and is closely related to the Alternating Direction Method of Multipliers (ADMM).  ... 
arXiv:1909.08600v2 fatcat:ktnanu2gszagvlktug7dbiaa7u

Fourier Ptychographic Microscopy via Alternating Direction Method of Multipliers

Aiye Wang, Zhuoqun Zhang, Siqi Wang, An Pan, Caiwen Ma, Baoli Yao
2022 Cells  
Herein, we utilized the concept of alternating direction method of multipliers (ADMM) to solve this problem (termed ADMM-FPM) by breaking it into multiple subproblems, each of which may be easier to deal  ...  Its reconstruction is normally formulated as a blind phase retrieval problem, where both the object and probe have to be recovered from phaseless measured data.  ...  Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/cells11091512 pmid:35563818 pmcid:PMC9104836 fatcat:kzsxgrwvtfb6zoq4o7kzwezipi

The Numerics of Phase Retrieval [article]

Albert Fannjiang, Thomas Strohmer
2020 arXiv   pre-print
Phase retrieval, i.e., the problem of recovering a function from the squared magnitude of its Fourier transform, arises in many applications such as X-ray crystallography, diffraction imaging, optics,  ...  Indeed, the last decade has witnessed a surge in the systematic study of computational algorithms for phase retrieval. In this paper we will review these recent advances from a numerical viewpoint.  ...  The description of these simulations and associated images are courtesy of [12] , which also contains a number of other simulations.  ... 
arXiv:2004.05788v1 fatcat:e375tjo26zeiladvkob37hgzwe

Evaluation of partial coherence correction in X-ray ptychography

Nicolas Burdet, Xiaowen Shi, Daniel Parks, Jesse N. Clark, Xiaojing Huang, Stephen D. Kevan, Ian K. Robinson
2015 Optics Express  
convergence.  ...  (degree of phase diversity of the probe) and sample phase complexity.  ...  Acknowledgments The work of XS, DP, and SK was partially supported by the U.S. Department  ... 
doi:10.1364/oe.23.005452 pmid:25836778 fatcat:pl2kxyjqyndqbgyxsikgdsfim4

Dynamic nanoimaging of extended objects via hard X-ray multiple-shot coherent diffraction with projection illumination optics

Yuki Takayama, Keizo Fukuda, Motoki Kawashima, Yuki Aoi, Daiki Shigematsu, Tatsuki Akada, Takumi Ikeda, Yasushi Kagoshima
2021 Communications Physics  
We developed projection illumination optics to produce a probe with a well-defined illumination area and a phase retrieval algorithm, establishing a spatio-temporal smoothness constraint for the reliable  ...  reconstruction of dynamic images.  ...  We thank Masashi Yoshimura of SPring-8 Service Co., Ltd. and Miho Manabe, Makoto Okamura, and Hinako Arisawa of the University of Hyogo for their assistance with the CDI experiments.  ... 
doi:10.1038/s42005-021-00539-x fatcat:wurbrtoydfg55f54h6uku7w3uu

Advanced denoising for X-ray ptychography

Huibin Chang, Pablo Enfedaque, Jie Zhang, Juliane Reinhardt, Bjoern Enders, Young-Sang Yu, David Shapiro, Christian G. Schroer, Tieyong Zeng, Stefano Marchesini
2019 Optics Express  
The success of ptychographic imaging experiments strongly depends on achieving high signal-to-noise ratio.  ...  We present a formal description of the proposed algorithm and prove its convergence under mild conditions.  ...  Averaged Alternating Reflections (RAAR [18] ) based algorithms [19] , and generalized Alternating Direction Method of Multipliers (ADMM) [20] [21] [22] ) based BP [15] .  ... 
doi:10.1364/oe.27.010395 fatcat:vujld73azrgobkcwurhqhhpdb4

Direct phase retrieval in double blind Fourier holography

Oren Raz, Ben Leshem, Jianwei Miao, Boaz Nadler, Dan Oron, Nirit Dudovich
2014 Optics Express  
Here we combine these two approaches and present a new scheme, termed double blind Fourier holography, providing an efficient solution to the phase problem in two dimensions, by solving a system of linear  ...  Phase measurement is a long-standing challenge in a wide range of applications, from X-ray imaging to astrophysics and spectroscopy.  ...  Via an SVD of this matrix we thus recover the unknown phase factors e iψ(x) and e −iφ (y) .  ... 
doi:10.1364/oe.22.024935 pmid:25401527 fatcat:fq2oio5by5d33b57b2om6p7lui

Phase-contrast imaging of multiply-scattering extended objects at atomic resolution by reconstruction of the scattering matrix

Philipp M. Pelz, Hamish G. Brown, Scott Stonemeyer, Scott D. Findlay, Alex Zettl, Peter Ercius, Yaqian Zhang, Jim Ciston, M. C. Scott, Colin Ophus
2021 Physical Review Research  
Three-dimensional phase-contrast imaging of multiply-scattering samples in x-ray and electron microscopy is challenging due to small numerical apertures, the unavailability of wave front shaping optics  ...  Our work enables phase contrast imaging and materials characterization in multiply-scattering samples at high resolution for a wide range of materials.  ...  More recently, Bayesian accelerated gradient methods [63] and methods based on the alternating direction method of multipliers (ADMM) [64] have become popular.  ... 
doi:10.1103/physrevresearch.3.023159 fatcat:vysh3eh7dvdqjbjp7uzxbed2e4

Reconstructing the Scattering Matrix from Scanning Electron Diffraction Measurements Alone [article]

Philipp M Pelz and Hamish G Brown and Jim Ciston and Scott D Findlay and Yaqian Zhang and Mary Scott and Colin Ophus
2020 arXiv   pre-print
Three-dimensional phase contrast imaging of multiply-scattering samples in X-ray and electron microscopy is extremely challenging, due to small numerical apertures, the unavailability of wavefront shaping  ...  Our method will enable 3D imaging and materials characterization at high resolution for a wide range of materials.  ...  More recently, Bayesian accelerated gradient methods [62] and methods based on the alternating direction method of multipliers (ADMM) [63] have become popular.  ... 
arXiv:2008.12768v1 fatcat:llrkwaz2bvhrlchmh3hqrs34p4

Common pulse retrieval algorithm: a fast and universal method to retrieve ultrashort pulses

Nils C. Geib, Matthias Zilk, Thomas Pertsch, Falk Eilenberger
2019 Optica  
These results improve and extend the possibilities of numerical pulse retrieval. COPRA is faster and provides more accurate results in comparison to existing retrieval algorithms.  ...  FROG, dispersion scan, time domain ptychography, and pulse shaper assisted techniques such as multiphoton intrapulse interference phase scan (MIIPS).  ...  For example, they are all ambiguous to the constant and linear phase ofẼ(ω). Some methods (e.g., SHG-FROG and SHG-iFROG) leave the direction of time undetermined.  ... 
doi:10.1364/optica.6.000495 fatcat:5gbqgmzpnfglndedeso3mde4qq

Proximal Methods for Image Processing [chapter]

D. Russell Luke
2020 Topics in applied physics  
ansatz, the second phase simultaneous phase retrieval and probe determination in what is essentially a nonlinear blind deconvolution.  ...  A quilt is a ptychogram of sorts. Or put in more technical terms, ptychography is a combination of blind deconvolution and computed tomography for phase retrieval.  ... 
doi:10.1007/978-3-030-34413-9_6 fatcat:jazwae5vsfeubgbci6zcwavvcu

A phase space model of Fourier ptychographic microscopy

Roarke Horstmeyer, Changhuei Yang
2014 Optics Express  
A new computational imaging technique, termed Fourier ptychographic microscopy (FPM), uses a sequence of low-resolution images captured under varied illumination to iteratively converge upon a high-resolution  ...  We hope this finding encourages the future cross-pollination of ideas between two otherwise unconnected experimental imaging procedures.  ...  Acknowledgments The authors acknowledge funding support from the National Institutes of Health (grant no. 1DP2OD007307-01) and Clearbridge Biophotonics Pte Ltd., Singapore (Agency Award no.  ... 
doi:10.1364/oe.22.000338 pmid:24514995 pmcid:PMC3926543 fatcat:mlaf4sahwbcnjnechtz5knxe7a
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