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A modified coherent diffraction algorithm based on the total variation algorithm for insufficient data

Funds:  Supported by National Key Research and Development Project of China (2017YFA0402904, 2016YFA0400902), National Natural Science Foundation of China (11475175, 11405175, 11275204,11775224).
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https://doi.org/10.3969/j.issn.0253-2778.2020.04.005
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  • Author Bio:

    JIANG Qi, male, born in 1994, master. Research field: Coherent diffraction imaging. E-mail: jqi1994@mail.ustc.edu.cn

  • Corresponding author: TIAN Yangchao
  • Received Date: 21 May 2019
  • Accepted Date: 22 June 2019
  • Rev Recd Date: 22 June 2019
  • Publish Date: 30 April 2020
    Abstract

  • Abstract

    X-ray coherent diffraction imaging (CDI) is a lensless imaging technology. Its basic principle is to illuminate an isolated sample with a highly coherent X-ray beam, then collect the information of the coherent diffraction pattern in the far field, and last restore the real structure information of the sample from the diffraction pattern by using the the CDI algorithm. Due to the limitation of experimental technology experimental data are usually defective, thus tolerance to noise and missing data is an important indicator for the CDI algorithm. Here a modified coherent diffraction algorithm by adding the total variation (TV) constraint into the CDI reconstruction algorithm was developed to improve the tolerance to noise and missing data. Then the performance of the modified coherent diffraction algorithm based on the total variation algorithm was verified using simulation data and experimental data. The results show the modified algorithm can accelerate convergence and improve the tolerance to noise and missing data.

    Abstract

    X-ray coherent diffraction imaging (CDI) is a lensless imaging technology. Its basic principle is to illuminate an isolated sample with a highly coherent X-ray beam, then collect the information of the coherent diffraction pattern in the far field, and last restore the real structure information of the sample from the diffraction pattern by using the the CDI algorithm. Due to the limitation of experimental technology experimental data are usually defective, thus tolerance to noise and missing data is an important indicator for the CDI algorithm. Here a modified coherent diffraction algorithm by adding the total variation (TV) constraint into the CDI reconstruction algorithm was developed to improve the tolerance to noise and missing data. Then the performance of the modified coherent diffraction algorithm based on the total variation algorithm was verified using simulation data and experimental data. The results show the modified algorithm can accelerate convergence and improve the tolerance to noise and missing data.
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    • References(17)
  • [1]
    MIAO J W, CHARALAMBOUS P, KIRZ J, et al. Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens[J]. Nature, 1999, 400: 342-344.
    [2]
    ROY M, SEO D, OH S, et al. A review of recent progress in lens-free imaging and sensing[J]. Biosensors and Bioelectronics, 2017, 88: 130-143.
    [3]
    JIANG H D, SONG C Y, CHEN C C, et al. Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy[J]. Proc Natl Acad Sci U S A, 2010, 107(25): 11234-11239.
    [4]
    MIAO J W, NISHINO Y, KOHMURA Y, et al. Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone[J]. Phys Rev Lett, 2005, 95(8): 085503.
    [5]
    CHAPMAN H N, NUGENT K A. Coherent lensless X-ray imaging[J]. Nat Photonics, 2010, 4(12): 833-839.
    [6]
    HUANG X J, NELSON J, STEINBRENER J, et al. Incorrect support and missing center tolerances of phasing algorithms[J]. Opt Express, 2010, 18(25): 26441-26449.
    [7]
    SHAPIRO D, THIBAULT P, BEETZ T, et al. Biological imaging by soft X-ray diffraction microscopy[J]. Proc Natl Acad Sci U S A, 2005, 102(43): 15343-15346.
    [8]
    FIENUP J R. Phase retrieval algorithms: A comparison[J]. Appl Optics, 1982, 21(15): 2758-2769.
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    RODRIGUEZ J A, XU R, CHEN C C, et al. Oversampling smoothness: An effective algorithm for phase retrieval of noisy diffraction intensities[J]. J Appl Crystallogr, 2013, 46: 312-318.
    [10]
    XU R, SALHA S, RAINES K S, et al. Coherent diffraction microscopy at SPring-8: Instrumentation, data acquisition and data analysis[J]. J Synchrot Radiat, 2011, 18: 293-298.
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    SIDKY E M, KAO C M, PAN X C. Accurate image reconstruction from few views and limitedangle data in divergentbeam CT[J]. J X-Ray Sci Technol, 2006, 14(2): 119-139.
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    VAN DER SCHOT G, SVENDA M, MAIA F, et al. Imaging single cells in a beam of live cyanobacteria with an X-ray laser[J]. Nat Commun, 2015, 6(9): 5704.
    [13]
    GERCHBERG R W, SAXTON W O. Practical algorithm for determination of phase from image and diffraction plane pictures[J]. Optik: International Journal for Light and Electron Optics, 1972, 35(2): 237-250.
    [14]
    FAN J D, SUN Z, ZHANG J, et al. Quantitative imaging of single unstained magnetotactic bacteria by coherent X-ray diffraction microscopy[J]. Anal Chem, 2015, 87(12): 5849-5853.
    [15]
    MIAO J W, HODGSON K O, ISHIKAWA T, et al. Imaging whole Escherichia coli bacteria by using single-particle X-ray diffraction[J]. Proc Natl Acad Sci U S A, 2003, 100(1): 110-112.
    [16]
    CHAPMAN H N, BARTY A, MARCHESINI S, et al. High-resolution ab initio three-dimensional X-ray diffraction microscopy[J] . J Opt Soc Am A: Opt Image Sci Vis, 2006, 23(5): 1179-1200.
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    PFEIFFER F. X-ray ptychography[J]. Nat Photonics, 2017, 12(1): 9-17. )
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    [1]
    MIAO J W, CHARALAMBOUS P, KIRZ J, et al. Extending the methodology of X-ray crystallography to allow imaging of micrometer-sized non-crystalline specimens[J]. Nature, 1999, 400: 342-344.
    [2]
    ROY M, SEO D, OH S, et al. A review of recent progress in lens-free imaging and sensing[J]. Biosensors and Bioelectronics, 2017, 88: 130-143.
    [3]
    JIANG H D, SONG C Y, CHEN C C, et al. Quantitative 3D imaging of whole, unstained cells by using X-ray diffraction microscopy[J]. Proc Natl Acad Sci U S A, 2010, 107(25): 11234-11239.
    [4]
    MIAO J W, NISHINO Y, KOHMURA Y, et al. Quantitative image reconstruction of GaN quantum dots from oversampled diffraction intensities alone[J]. Phys Rev Lett, 2005, 95(8): 085503.
    [5]
    CHAPMAN H N, NUGENT K A. Coherent lensless X-ray imaging[J]. Nat Photonics, 2010, 4(12): 833-839.
    [6]
    HUANG X J, NELSON J, STEINBRENER J, et al. Incorrect support and missing center tolerances of phasing algorithms[J]. Opt Express, 2010, 18(25): 26441-26449.
    [7]
    SHAPIRO D, THIBAULT P, BEETZ T, et al. Biological imaging by soft X-ray diffraction microscopy[J]. Proc Natl Acad Sci U S A, 2005, 102(43): 15343-15346.
    [8]
    FIENUP J R. Phase retrieval algorithms: A comparison[J]. Appl Optics, 1982, 21(15): 2758-2769.
    [9]
    RODRIGUEZ J A, XU R, CHEN C C, et al. Oversampling smoothness: An effective algorithm for phase retrieval of noisy diffraction intensities[J]. J Appl Crystallogr, 2013, 46: 312-318.
    [10]
    XU R, SALHA S, RAINES K S, et al. Coherent diffraction microscopy at SPring-8: Instrumentation, data acquisition and data analysis[J]. J Synchrot Radiat, 2011, 18: 293-298.
    [11]
    SIDKY E M, KAO C M, PAN X C. Accurate image reconstruction from few views and limitedangle data in divergentbeam CT[J]. J X-Ray Sci Technol, 2006, 14(2): 119-139.
    [12]
    VAN DER SCHOT G, SVENDA M, MAIA F, et al. Imaging single cells in a beam of live cyanobacteria with an X-ray laser[J]. Nat Commun, 2015, 6(9): 5704.
    [13]
    GERCHBERG R W, SAXTON W O. Practical algorithm for determination of phase from image and diffraction plane pictures[J]. Optik: International Journal for Light and Electron Optics, 1972, 35(2): 237-250.
    [14]
    FAN J D, SUN Z, ZHANG J, et al. Quantitative imaging of single unstained magnetotactic bacteria by coherent X-ray diffraction microscopy[J]. Anal Chem, 2015, 87(12): 5849-5853.
    [15]
    MIAO J W, HODGSON K O, ISHIKAWA T, et al. Imaging whole Escherichia coli bacteria by using single-particle X-ray diffraction[J]. Proc Natl Acad Sci U S A, 2003, 100(1): 110-112.
    [16]
    CHAPMAN H N, BARTY A, MARCHESINI S, et al. High-resolution ab initio three-dimensional X-ray diffraction microscopy[J] . J Opt Soc Am A: Opt Image Sci Vis, 2006, 23(5): 1179-1200.
    [17]
    PFEIFFER F. X-ray ptychography[J]. Nat Photonics, 2017, 12(1): 9-17. )
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