Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval

Fung, Samy Wu; Di, Zichao (Wendy)

doi:10.1137/18m1223915

Title: Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval

Abstract

Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. Herein, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community.

Authors:

^[1]; Di, Zichao ^[2]

Emory Univ., Atlanta, GA (United States)
(Wendy) [Argonne National Lab. (ANL), Lemont, IL (United States)

Publication Date:: 2020-02-19

Research Org.:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1660755

Report Number(s):: P9139-1018
Journal ID: ISSN 1936-4954; 154026

Grant/Contract Number:: AC02-06CH11357

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Imaging Sciences

Additional Journal Information:: Journal Volume: 13; Journal Issue: 1; Journal ID: ISSN 1936-4954

Publisher:: Society for Industrial and Applied Mathematics

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; coherent diffraction imaging; inverse problems; multigrid optimization; phase retrieval; ptychography

Citation Formats


                    Fung, Samy Wu, and Di, Zichao. Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval.  United States: N. p., 2020. 
Web.  doi:10.1137/18m1223915.

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                    Fung, Samy Wu, & Di, Zichao. Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval.  United States.  https://doi.org/10.1137/18m1223915

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                    Fung, Samy Wu, and Di, Zichao. Wed .  
"Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval".  United States.  https://doi.org/10.1137/18m1223915.  https://www.osti.gov/servlets/purl/1660755.

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@article{osti_1660755,

  title        = {Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval},

  author       = {Fung, Samy Wu and Di, Zichao},

  abstractNote = {Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and improved reconstructions. Ptychographic microscopes allow for large fields to be imaged at high resolution at the cost of additional computational expense. Herein, we propose a multigrid-based optimization framework to reduce the computational burdens of large-scale ptychographic phase retrieval. Our proposed method exploits the inherent hierarchical structures in ptychography through tailored restriction and prolongation operators for the object and data domains. Our numerical results show that our proposed scheme accelerates the convergence of its underlying solver and outperforms the ptychographical iterative engine, a workhorse in the optics community.},

  doi          = {10.1137/18m1223915},

  journal      = {SIAM Journal on Imaging Sciences},

  number       = 1,

  volume       = 13,

  place        = {United States},

  year         = {2020},

  month        = {2}

}

Copy to clipboard

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Similar Records

Title: Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval

Abstract

Citation Formats

Iterative Algorithms for Ptychographic Phase Retrieval preprint, January 2011

Microscopic imaging of biological samples using coherent soft X-rays from free-electron laser and synchrotron sources text, January 2011

Unconstrained Optimization of Real Functions in Complex Variables journal, January 2012

Algorithms for reconstruction of partially known, band-limited Fourier-transform pairs from noisy data journal, November 1985

A complex gradient operator and its application in adaptive array theory journal, January 1983

Influence of the overlap parameter on the convergence of the ptychographical iterative engine journal, April 2008

Phase Retrieval via Matrix Completion journal, January 2015

Phase Retrieval via Wirtinger Flow: Theory and Algorithms journal, April 2015

Total Variation--Based Phase Retrieval for Poisson Noise Removal journal, January 2018

Ptychographic Imaging of Branched Colloidal Nanocrystals Embedded in Free-Standing Thick Polystyrene Films journal, January 2016

Phase retrieval algorithms: a comparison journal, January 1982

Direct coupling of tomography and ptychography journal, January 2017

Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging journal, January 2015

High-resolution non-destructive three-dimensional imaging of integrated circuits journal, March 2017

High-resolution chemical imaging of gold nanoparticles using hard x-ray ptychography journal, May 2013

Optimization of overlap uniformness for ptychography journal, January 2014

Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm journal, December 2016

Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations journal, January 2005

Optical Wavefront Reconstruction: Theory and Numerical Methods journal, January 2002

Globally Convergent Levenberg-Marquardt Method for Phase Retrieval journal, April 2019

Further improvements to the ptychographical iterative engine journal, January 2017

An improved ptychographical phase retrieval algorithm for diffractive imaging journal, September 2009

Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval journal, January 2007

Ptychography – a label free, high-contrast imaging technique for live cells using quantitative phase information journal, August 2013

Preconditioning of Truncated-Newton Methods journal, July 1985

A multigrid approach to discretized optimization problems journal, January 2000

Parallel ptychographic reconstruction journal, January 2014

On-the-fly scans for X-ray ptychography journal, December 2014

A phase retrieval algorithm for shifting illumination journal, November 2004

Multilevel Gauss–Newton methods for phase retrieval problems journal, March 2006

Unconstrained Optimization of Real Functions in Complex Variables journal, January 2012

Dark-field X-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens journal, October 2016

Probe retrieval in ptychographic coherent diffractive imaging journal, March 2009

Maximum-likelihood refinement for coherent diffractive imaging journal, June 2012

Image Quality Assessment: From Error Visibility to Structural Similarity journal, April 2004

Alternating direction methods for classical and ptychographic phase retrieval journal, October 2012

Experimental robustness of Fourier ptychography phase retrieval algorithms journal, January 2015

Iterative Algorithms for Ptychographic Phase Retrieval
preprint, January 2011

Microscopic imaging of biological samples using coherent soft X-rays from free-electron laser and synchrotron sources
text, January 2011

Unconstrained Optimization of Real Functions in Complex Variables
journal, January 2012

Algorithms for reconstruction of partially known, band-limited Fourier-transform pairs from noisy data
journal, November 1985

A complex gradient operator and its application in adaptive array theory
journal, January 1983

Influence of the overlap parameter on the convergence of the ptychographical iterative engine
journal, April 2008

Phase Retrieval via Matrix Completion
journal, January 2015

Phase Retrieval via Wirtinger Flow: Theory and Algorithms
journal, April 2015

Total Variation--Based Phase Retrieval for Poisson Noise Removal
journal, January 2018

Ptychographic Imaging of Branched Colloidal Nanocrystals Embedded in Free-Standing Thick Polystyrene Films
journal, January 2016

Phase retrieval algorithms: a comparison
journal, January 1982

Direct coupling of tomography and ptychography
journal, January 2017

Proximal Heterogeneous Block Implicit-Explicit Method and Application to Blind Ptychographic Diffraction Imaging
journal, January 2015

High-resolution non-destructive three-dimensional imaging of integrated circuits
journal, March 2017

High-resolution chemical imaging of gold nanoparticles using hard x-ray ptychography
journal, May 2013

Optimization of overlap uniformness for ptychography
journal, January 2014

Combining ptychographical algorithms with the Hybrid Input-Output (HIO) algorithm
journal, December 2016

Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations
journal, January 2005

Optical Wavefront Reconstruction: Theory and Numerical Methods
journal, January 2002

Globally Convergent Levenberg-Marquardt Method for Phase Retrieval
journal, April 2019

Further improvements to the ptychographical iterative engine
journal, January 2017

An improved ptychographical phase retrieval algorithm for diffractive imaging
journal, September 2009

Invited Article: A unified evaluation of iterative projection algorithms for phase retrieval
journal, January 2007

Ptychography – a label free, high-contrast imaging technique for live cells using quantitative phase information
journal, August 2013

Preconditioning of Truncated-Newton Methods
journal, July 1985

A multigrid approach to discretized optimization problems
journal, January 2000

Parallel ptychographic reconstruction
journal, January 2014

On-the-fly scans for X-ray ptychography
journal, December 2014

A phase retrieval algorithm for shifting illumination
journal, November 2004

Multilevel Gauss–Newton methods for phase retrieval problems
journal, March 2006

Unconstrained Optimization of Real Functions in Complex Variables
journal, January 2012

Dark-field X-ray ptychography: Towards high-resolution imaging of thick and unstained biological specimens
journal, October 2016

Probe retrieval in ptychographic coherent diffractive imaging
journal, March 2009

Maximum-likelihood refinement for coherent diffractive imaging
journal, June 2012

Image Quality Assessment: From Error Visibility to Structural Similarity
journal, April 2004

Alternating direction methods for classical and ptychographic phase retrieval
journal, October 2012

Experimental robustness of Fourier ptychography phase retrieval algorithms
journal, January 2015