Denoised Wigner distribution deconvolution via low-rank matrix completion

Lee, Justin; Barbastathis, George

doi:10.1364/OE.24.020069

Denoised Wigner distribution deconvolution via low-rank matrix completion

Journal Article · Tue Aug 23 00:00:00 EDT 2016 · Optics Express

DOI:https://doi.org/10.1364/OE.24.020069· OSTI ID:1434528

Lee, Justin ^[1]; Barbastathis, George ^[2]

Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Health Sciences and Technology; None
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Mechanical Engineering; Singapore-MIT Alliance for Research and Technology (SMART) Centre (Singapore)

Wigner distribution deconvolution (WDD) is a decades-old method for recovering phase from intensity measurements. Although the technique offers an elegant linear solution to the quadratic phase retrieval problem, it has seen limited adoption due to its high computational/memory requirements and the fact that the technique often exhibits high noise sensitivity. Here, we propose a method for noise suppression in WDD via low-rank noisy matrix completion. Our technique exploits the redundancy of an object’s phase space to denoise its WDD reconstruction. We show in model calculations that our technique outperforms other WDD algorithms as well as modern iterative methods for phase retrieval such as ptychography. Here, our results suggest that a class of phase retrieval techniques relying on regularized direct inversion of ptychographic datasets (instead of iterative reconstruction techniques) can provide accurate quantitative phase information in the presence of high levels of noise.

View Accepted Manuscript (DOE)

Research Organization:: Krell Inst., Ames, IA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: FG02-97ER25308

OSTI ID:: 1434528

Journal Information:: Optics Express, Journal Name: Optics Express Journal Issue: 18 Vol. 24; ISSN 1094-4087; ISSN OPEXFF

Publisher:: Optical Society of America (OSA)Copyright Statement

Country of Publication:: United States

Language:: English

References (17)

Exact Matrix Completion via Convex Optimization Candès, Emmanuel J.; Recht, Benjamin Foundations of Computational Mathematics, Vol. 9, Issue 6 https://doi.org/10.1007/s10208-009-9045-5	journal	April 2009
Sub-ångström transmission microscopy: A fourier transform algorithm for microdiffraction plane intensity information Bates, R. H. T.; Rodenburg, J. M. Ultramicroscopy, Vol. 31, Issue 3 https://doi.org/10.1016/0304-3991(89)90052-1	journal	November 1989
Two-dimensional demonstration of Wigner phase-retrieval microscopy in the STEM configuration McCallum, B. C.; Rodenburg, J. M. Ultramicroscopy, Vol. 45, Issue 3-4 https://doi.org/10.1016/0304-3991(92)90149-E	journal	November 1992
Experimental tests on double-resolution coherent imaging via STEM Rodenburg, J. M.; McCallum, B. C.; Nellist, P. D. Ultramicroscopy, Vol. 48, Issue 3 https://doi.org/10.1016/0304-3991(93)90105-7	journal	March 1993
Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution Chapman, Henry N. Ultramicroscopy, Vol. 66, Issue 3-4 https://doi.org/10.1016/S0304-3991(96)00084-8	journal	December 1996
Ptychographic inversion via Wigner distribution deconvolution: Noise suppression and probe design Li, Peng; Edo, Tega B.; Rodenburg, John M. Ultramicroscopy, Vol. 147 https://doi.org/10.1016/j.ultramic.2014.07.004	journal	December 2014
Soft X-ray spectromicroscopy using ptychography with randomly phased illumination Maiden, A. M.; Morrison, G. R.; Kaulich, B. Nature Communications, Vol. 4, Issue 1 https://doi.org/10.1038/ncomms2640	journal	April 2013
Wide-field, high-resolution Fourier ptychographic microscopy Zheng, Guoan; Horstmeyer, Roarke; Yang, Changhuei Nature Photonics, Vol. 7, Issue 9 https://doi.org/10.1038/nphoton.2013.187	journal	July 2013
Maximum-likelihood refinement for coherent diffractive imaging Thibault, P.; Guizar-Sicairos, M. New Journal of Physics, Vol. 14, Issue 6 https://doi.org/10.1088/1367-2630/14/6/063004	journal	June 2012
The theory of super-resolution electron microscopy via Wigner-distribution deconvolution Rodenburg, J. M.; Bates, R. H. T. Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences, Vol. 339, Issue 1655, p. 521-553 https://doi.org/10.1098/rsta.1992.0050	journal	June 1992
Matrix Completion With Noise Candes, Emmanuel J.; Plan, Yaniv Proceedings of the IEEE, Vol. 98, Issue 6 https://doi.org/10.1109/JPROC.2009.2035722	journal	June 2010
A Singular Value Thresholding Algorithm for Matrix Completion Cai, Jian-Feng; Candès, Emmanuel J.; Shen, Zuowei SIAM Journal on Optimization, Vol. 20, Issue 4 https://doi.org/10.1137/080738970	journal	January 2010
Superresolution imaging via ptychography Maiden, Andrew M.; Humphry, Martin J.; Zhang, Fucai Journal of the Optical Society of America A, Vol. 28, Issue 4 https://doi.org/10.1364/JOSAA.28.000604	journal	January 2011
Phase retrieval with transverse translation diversity: a nonlinear optimization approach Guizar-Sicairos, Manuel; Fienup, James R. Optics Express, Vol. 16, Issue 10 https://doi.org/10.1364/OE.16.007264	journal	January 2008
Noise models for low counting rate coherent diffraction imaging Godard, Pierre; Allain, Marc; Chamard, Virginie Optics Express, Vol. 20, Issue 23 https://doi.org/10.1364/OE.20.025914	journal	January 2012
Experimental robustness of Fourier ptychography phase retrieval algorithms Yeh, Li-Hao; Dong, Jonathan; Zhong, Jingshan Optics Express, Vol. 23, Issue 26 https://doi.org/10.1364/OE.23.033214	journal	January 2015
Elementary signals in ptychography da Silva, Julio Cesar; Menzel, Andreas Optics Express, Vol. 23, Issue 26 https://doi.org/10.1364/OE.23.033812	journal	January 2015

Cited By (2)

Electron ptychography of 2D materials to deep sub-ångström resolution Jiang, Yi; Chen, Zhen; Han, Yimo Nature, Vol. 559, Issue 7714 https://doi.org/10.1038/s41586-018-0298-5	journal	July 2018
On the use of deep learning for computational imaging Barbastathis, George; Ozcan, Aydogan; Situ, Guohai Optica, Vol. 6, Issue 8 https://doi.org/10.1364/optica.6.000921	journal	January 2019

Similar Records

Multigrid Optimization for Large-Scale Ptychographic Phase Retrieval

Journal Article · Tue Feb 18 19:00:00 EST 2020 · SIAM Journal on Imaging Sciences · OSTI ID:1660755

A novel partial volume effects correction technique integrating deconvolution associated with denoising within an iterative PET image reconstruction

Journal Article · Sat Feb 14 23:00:00 EST 2015 · Medical Physics · OSTI ID:22413446

Related Subjects

47 OTHER INSTRUMENTATION
Image reconstruction techniques
Noise in imaging systems
Phase retrieval
X-ray imaging

Denoised Wigner distribution deconvolution via low-rank matrix completion

Citation Formats

References (17)

Cited By (2)

Similar Records

Related Subjects