Free log-likelihood as an unbiased metric for coherent diffraction imaging.
Journal
Scientific reports
ISSN: 2045-2322
Titre abrégé: Sci Rep
Pays: England
ID NLM: 101563288
Informations de publication
Date de publication:
14 02 2020
14 02 2020
Historique:
received:
20
09
2019
accepted:
16
12
2019
entrez:
16
2
2020
pubmed:
16
2
2020
medline:
16
2
2020
Statut:
epublish
Résumé
Coherent Diffraction Imaging (CDI), a technique where an object is reconstructed from a single (2D or 3D) diffraction pattern, recovers the lost diffraction phases without a priori knowledge of the extent (support) of the object. The uncertainty of the object support can lead to over-fitting and prevents an unambiguous metric evaluation of solutions. We propose to use a 'free' log-likelihood indicator, where a small percentage of points are masked from the reconstruction algorithms, as an unbiased metric to evaluate the validity of computed solutions, independent of the sample studied. We also show how a set of solutions can be analysed through an eigen-decomposition to yield a better estimate of the real object. Example analysis on experimental data is presented both for a test pattern dataset, and the diffraction pattern from a live cyanobacteria cell. The method allows the validation of reconstructions on a wide range of materials (hard condensed or biological), and should be particularly relevant for 4th generation synchrotrons and X-ray free electron lasers, where large, high-throughput datasets require a method for unsupervised data evaluation.
Identifiants
pubmed: 32060293
doi: 10.1038/s41598-020-57561-2
pii: 10.1038/s41598-020-57561-2
pmc: PMC7021796
doi:
Types de publication
Journal Article
Langues
eng
Sous-ensembles de citation
IM
Pagination
2664Références
Sayre, D., Chapman, H. N. & Miao, J. On the extendibility of X-ray crystallography to noncrystals. Acta Crystallogr. Sect. A: Foundations Crystallogr. 54, 232–239 (1998).
doi: 10.1107/S0108767397015572
Miao, J., Charalambous, P., Kirz, J. & Sayre, D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 400, 342–344, https://doi.org/10.1038/22498 (1999).
doi: 10.1038/22498
Miao, J. & Sayre, D. On possible extensions of X-ray crystallography through diffraction-pattern oversampling. Acta Crystallogr. Sect. A Foundations Crystallogr. 56, 596–605, https://doi.org/10.1107/S010876730001031X (2000).
doi: 10.1107/S010876730001031X
Miao, J., Hodgson, K. O. & Sayre, D. An approach to three-dimensional structures of biomolecules by using singlemolecule diffraction images. PNAS 98, 6641–6645, https://doi.org/10.1073/pnas.111083998 (2001).
doi: 10.1073/pnas.111083998
pubmed: 11390993
Marchesini, S. et al. X-ray image reconstruction from a diffraction pattern alone. Phys. Rev. B. 68, 140101, https://doi.org/10.1103/PhysRevB.68.140101 (2003).
doi: 10.1103/PhysRevB.68.140101
Sandberg, R. L. et al. Lensless Diffractive Imaging Using Tabletop Coherent High-Harmonic Soft-X-Ray Beams. Phys. Rev. Lett. 99, 098103, https://doi.org/10.1103/PhysRevLett.99.098103 (2007).
doi: 10.1103/PhysRevLett.99.098103
pubmed: 17931040
Zuo, J. M., Vartanyants, I., Gao, M., Zhang, R. & Nagahara, L. A. Atomic Resolution Imaging of a Carbon Nanotube from Diffraction Intensities. Science 300, 1419–1421, https://doi.org/10.1126/science.1083887 (2003).
doi: 10.1126/science.1083887
pubmed: 12775837
Huang, W. J. et al. Coordination-dependent surface atomic contraction in nanocrystals revealed by coherent diffraction. Nat Mater 7, 308–313, https://doi.org/10.1038/nmat2132 (2008).
doi: 10.1038/nmat2132
pubmed: 18327263
Robinson, I. K., Vartanyants, I. A., Williams, G. J., Pfeifer, M. A. & Pitney, J. A. Reconstruction of the Shapes of Gold Nanocrystals Using Coherent X-Ray Diffraction. Phys. Rev. Lett. 87, 195505, https://doi.org/10.1103/PhysRevLett.87.195505 (2001).
doi: 10.1103/PhysRevLett.87.195505
pubmed: 11690423
Williams, G. J., Pfeifer, M. A., Vartanyants, I. A. & Robinson, I. K. Three-Dimensional Imaging of Microstructure in Au Nanocrystals. Phys. Rev. Lett. 90, 175501, https://doi.org/10.1103/PhysRevLett.90.175501 (2003).
doi: 10.1103/PhysRevLett.90.175501
pubmed: 12786079
Pfeifer, M. A., Williams, G. J., Vartanyants, I. A., Harder, R. & Robinson, I. K. Three-dimensional mapping of a deformation field inside a nanocrystal. Nature 442, 63–66, https://doi.org/10.1038/nature04867 (2006).
doi: 10.1038/nature04867
pubmed: 16823449
Favre-Nicolin, V. et al. Analysis of strain and stacking faults in single nanowires using Bragg coherent diffraction imaging. New J. Phys. 12, 035013, https://doi.org/10.1088/1367-2630/12/3/035013 (2010).
doi: 10.1088/1367-2630/12/3/035013
Robinson, I. & Harder, R. Coherent X-ray diffraction imaging of strain at the nanoscale. Nat Mater 8, 291–298, https://doi.org/10.1038/nmat2400 (2009).
doi: 10.1038/nmat2400
pubmed: 19308088
Shapiro, D. et al. Biological imaging by soft x-ray diffraction microscopy. PNAS 102, 15343–15346, https://doi.org/10.1073/pnas.0503305102 (2005).
doi: 10.1073/pnas.0503305102
pubmed: 16219701
Chushkin, Y. et al. Three-dimensional coherent diffractive imaging on non-periodic specimens at the ESRF beamline ID10. J. Synchrotron Radiat. 21, 594–599, https://doi.org/10.1107/S1600577514003440 (2014).
doi: 10.1107/S1600577514003440
pubmed: 24763650
Beuvier, T. et al. X-ray nanotomography of coccolithophores reveals that coccolith mass and segment number correlate with grid size. Nat. Commun. 10, 751, https://doi.org/10.1038/s41467-019-08635-x (2019).
doi: 10.1038/s41467-019-08635-x
pubmed: 30765698
pmcid: 6375944
Seibert, M. M. et al. Single mimivirus particles intercepted and imaged with an X-ray laser. Nature 470, 78–81, https://doi.org/10.1038/nature09748 (2011).
doi: 10.1038/nature09748
pubmed: 21293374
pmcid: 4038304
Clark, J. N. et al. Ultrafast Three-Dimensional Imaging of Lattice Dynamics in Individual Gold Nanocrystals. Science 341, 56–59, https://doi.org/10.1126/science.1236034 (2013).
doi: 10.1126/science.1236034
pubmed: 23704372
Sayre, D. Some implications of a theorem due to Shannon. Acta Crystallogr. 5, 843–843, https://doi.org/10.1107/S0365110X52002276 (1952).
doi: 10.1107/S0365110X52002276
Marchesini, S. A unified evaluation of iterative projection algorithms for phase retrieval. Rev. Sci. Instruments 78, 011301, https://doi.org/10.1063/1.2403783 (2007).
doi: 10.1063/1.2403783
Fienup, J. R. Phase retrieval algorithms: a personal tour [Invited]. Appl. Opt. 52, 45, https://doi.org/10.1364/AO.52.000045 (2013).
doi: 10.1364/AO.52.000045
pubmed: 23292374
Favre-Nicolin, V. Free log-likelihood as an unbiased metric for coherent diffraction imaging: figures and data, https://doi.org/10.5281/zenodo.3451855 (2019).
Thibault, P. & Guizar-Sicairos, M. Maximum-likelihood refinement for coherent diffractive imaging. New J. Phys. 14, 063004, https://doi.org/10.1088/1367-2630/14/6/063004 (2012).
doi: 10.1088/1367-2630/14/6/063004
Chapman, H. N. et al. High-resolution ab initio three-dimensional x-ray diffraction microscopy. J. Opt. Soc. Am. A 23, 1179–1200, https://doi.org/10.1364/JOSAA.23.001179 (2006).
doi: 10.1364/JOSAA.23.001179
Latychevskaia, T., Chushkin, Y., Zontone, F. & Fink, H.-W. Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns. Appl. Phys. Lett. 107, 183102, https://doi.org/10.1063/1.4934879 (2015).
doi: 10.1063/1.4934879
Devaney, A. J. & Chidlaw, R. On the uniqueness question in the problem of phase retrieval from intensity measurements. J. Opt. Soc. Am. 68, 1352–1354, https://doi.org/10.1364/JOSA.68.001352 (1978).
doi: 10.1364/JOSA.68.001352
Crimmins, T. R. & Fienup, J. R. Ambiguity of phase retrieval for functions with disconnected support. J. Opt. Soc. Am. 71, 1026–1028, https://doi.org/10.1364/JOSA.71.001026 (1981).
doi: 10.1364/JOSA.71.001026
Bates, R. H. T. Fourier phase problems are uniquely solvable in mute than one dimension. I: Underlying theory. Optik 61, 247 (1982).
Hayes, M. The reconstruction of a multidimensional sequence from the phase or magnitude of its Fourier transform. IEEE Transactions on Acoust. Speech. Signal Process. 30, 140–154, https://doi.org/10.1109/TASSP.1982.1163863 (1982).
doi: 10.1109/TASSP.1982.1163863
Bates, R. Uniqueness of solutions to two-dimensional fourier phase problems for localized and positive images. Comput. Vision, Graph. Image Process. 25, 205–217, https://doi.org/10.1016/0734-189X(84)90103-8 (1984).
doi: 10.1016/0734-189X(84)90103-8
Seldin, J. H. & Fienup, J. R. Numerical investigation of the uniqueness of phase retrieval. J. Opt. Soc. Am. A 7, 412, https://doi.org/10.1364/JOSAA.7.000412 (1990).
doi: 10.1364/JOSAA.7.000412
Ulvestad, A. et al. Identifying Defects with Guided Algorithms in Bragg Coherent Diffractive Imaging. Sci. Reports 7, 9920, https://doi.org/10.1038/s41598-017-09582-7 (2017).
doi: 10.1038/s41598-017-09582-7
Schülli, T. U. & Leake, S. J. X-ray nanobeam diffraction imaging of materials. Curr. Opin. Solid State Mater. Sci. 22, 188–201, https://doi.org/10.1016/j.cossms.2018.09.003 (2018).
doi: 10.1016/j.cossms.2018.09.003
Björling, A. et al. Coherent Bragg imaging of 60 nm Au nanoparticles under electrochemical control at the NanoMAX beamline. J Synchrotron Rad 26, 1830–1834, https://doi.org/10.1107/S1600577519010385 (2019).
doi: 10.1107/S1600577519010385
Brünger, A. T. Free R value: a novel statistical quantity for assessing the accuracy of crystal structures. Nature 355, 472–475, https://doi.org/10.1038/355472a0 (1992).
doi: 10.1038/355472a0
pubmed: 18481394
Tickle, I. J., Laskowski, R. A. & Moss, D. S. Rfree and the Rfree Ratio. I. Derivation of Expected Values of Cross-Validation Residuals Used in Macromolecular Least-Squares Refinement. Acta Crystallogr. Sect. D Biol. Crystallogr. 54, 547–557, https://doi.org/10.1107/S0907444997013875 (1998).
doi: 10.1107/S0907444997013875
Tickle, I. J., Laskowski, R. A. & Moss, D. S. Rfree and the Rfree ratio. II. Calculation of the expected values and variances of cross-validation statistics in macromolecular least-squares refinement. Acta Crystallogr. Sect. D Biol. Crystallogr. 56, 442–450, https://doi.org/10.1107/S0907444999016868 (2000).
doi: 10.1107/S0907444999016868
Quenouille, M. H. Problems in Plane Sampling. The Annals Math. Stat. 20, 355–375, https://doi.org/10.1214/aoms/1177729989 (1949).
doi: 10.1214/aoms/1177729989
Efron, B. & Stein, C. The Jackknife Estimate of Variance. The Annals Stat. 9, 586–596, https://doi.org/10.1214/aos/1176345462 (1981).
doi: 10.1214/aos/1176345462
Favre-Nicolin, V. PyNX, Python tools for Nanostructure Xtallography and coherent X-ray imaging, http://ftp.esrf.fr/pub/scisoft/PyNX/ (2010).
Miao, J., Kirz, J. & Sayre, D. The oversampling phasing method. Acta Crystallogr. Sect. D Biol. Crystallogr. 56, 1312–1315, https://doi.org/10.1107/S0907444900008970 (2000).
doi: 10.1107/S0907444900008970
Virtanen, P. et al. SciPy 1.0–Fundamental Algorithms for Scientific Computing in Python. arXiv:1907.10121 [physics] (2019). ArXiv: 1907.10121.
Guizar-Sicairos, M., Thurman, S. T. & Fienup, J. R. Efficient subpixel image registration algorithms. Opt. Letters 33, 156–158 (2008).
doi: 10.1364/OL.33.000156
Miao, J. et al. Imaging whole Escherichia coli bacteria by using single-particle x-ray diffraction. Proc. Natl. Acad. Sci. 100, 110–112, https://doi.org/10.1073/pnas.232691299 (2003).
doi: 10.1073/pnas.232691299
pubmed: 12518059
Thibault, P., Elser, V., Jacobsen, C., Shapiro, D. & Sayre, D. Reconstruction of a yeast cell from X-ray diffraction data. Acta Crystallogr. Sect. A Foundations Crystallogr. 62, 248–261, https://doi.org/10.1107/S0108767306016515 (2006).
doi: 10.1107/S0108767306016515
Nelson, J. et al. High-resolution x-ray diffraction microscopy of specifically labeled yeast cells. PNAS 107, 7235–7239, https://doi.org/10.1073/pnas.0910874107 (2010).
doi: 10.1073/pnas.0910874107
pubmed: 20368463
van der Schot, G. et al. Imaging single cells in a beam of live cyanobacteria with an X-ray laser. Nat Commun 6, 5704, https://doi.org/10.1038/ncomms6704 (2015).
doi: 10.1038/ncomms6704
pubmed: 25669616
Maia, F. R. N. C. The Coherent X-ray Imaging Data Bank. Nat. Methods 9, 854–855, https://doi.org/10.1038/nmeth.2110 (2012).
doi: 10.1038/nmeth.2110
pubmed: 22936162
Schot, G. Imaging single cells in a beam of live cyanobacteria with an X-ray laser (CXIDB ID 26), https://doi.org/10.11577/1169686 (2015). Type: dataset.
Enders, B. & Thibault, P. A computational framework for ptychographic reconstructions. Proc. Math Phys. Eng. Sci. 472, https://doi.org/10.1098/rspa.2016.0640 (2016).
doi: 10.1098/rspa.2016.0640