OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 20, Iss. 12 — Jun. 4, 2012
  • pp: 12827–12849

The symmetries of image formation by scattering. II. Applications

Peter Schwander, Dimitrios Giannakis, Chun Hong Yoon, and Abbas Ourmazd  »View Author Affiliations

Optics Express, Vol. 20, Issue 12, pp. 12827-12849 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (3430 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach constitutes a physically-based, computationally efficient, and noise-robust route to analyzing the large and varied datasets generated by existing and emerging methods for studying structure and dynamics by scattering. We demonstrate three-dimensional structure recovery from X-ray diffraction and cryo-electron microscope image snapshots of unknown orientation, the latter at 12 times lower dose than currently in use. We also show that ultra-low-signal, random sightings of dynamically evolving systems can be sequenced into high quality movies to reveal their evolution. Our approach offers a route to recovering timing information in time-resolved experiments, and extracting 3D movies from two-dimensional random sightings of dynamic systems.

© 2012 OSA

OCIS Codes
(140.2600) Lasers and laser optics : Free-electron lasers (FELs)
(180.6900) Microscopy : Three-dimensional microscopy
(290.3200) Scattering : Inverse scattering
(290.5840) Scattering : Scattering, molecules
(290.5825) Scattering : Scattering theory

ToC Category:

Original Manuscript: February 9, 2012
Revised Manuscript: May 11, 2012
Manuscript Accepted: May 16, 2012
Published: May 23, 2012

Peter Schwander, Dimitrios Giannakis, Chun Hong Yoon, and Abbas Ourmazd, "The symmetries of image formation by scattering. II. Applications," Opt. Express 20, 12827-12849 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. D. Giannakis, P. Schwander, and A. Ourmazd, “The symmetries of image formation by scattering. I. Theoretical framework,” Opt. Express (2012). Submitted.
  2. V. L. Shneerson, A. Ourmazd, and D. K. Saldin, “Crystallography without crystals. i. the common-line method for assembling a 3D diffraction volume from single-particle scattering,” Acta Cryst. A64, 303–315 (2008). [CrossRef]
  3. R. Fung, V. Shneerson, D. K. Saldin, and A. Ourmazd, “Structure from fleeting illumination of faint spinning objects in flight,” Nat. Phys.5, 64–67 (2008). [CrossRef]
  4. P. Schwander, R. Fung, G. N. Phillips, and A. Ourmazd, “Mapping the conformations of biological assemblies,” New J. Phys.12, 1–15 (2010). [CrossRef]
  5. http://www.youtube.com/watch?v=vqQfARtnsWw .
  6. http://www.youtube.com/watch?v=hbFiNaire4o .
  7. http://www.youtube.com/watch?v=unnHKBCT8XQ .
  8. http://www.youtube.com/watch?v=9Y2DF-X5LSA .
  9. J. Frank, “Single-particle imaging of macromolecules by cryo-electron microscopy,” Annu. Rev. Biophys. Biomolec. Struct.31, 303–319 (2002). [CrossRef]
  10. S. H. W. Scheres, H. Gao, M. Valle, G. T. Herman, P. P. B. Eggermont, J. Frank, and J.-M. Carazo, “Disentangling conformational states of macromolecules in 3D-EM through likelihood optimization,” Nature Methods4, 27–29 (2007). [CrossRef]
  11. N. T. D. Loh and V. Elser, “Reconstruction algorithm for single-particle diffraction imaging experiments,” Phys. Rev. E80, 026705 (2009). [CrossRef]
  12. N. Fischer, A. L. Konevega, W. Wintermeyer, M. V. Rodnina, and H. Stark, “Ribosome dynamics and tRNA movement by time-resolved electron cryomicroscopy.” Nature466, 329–333 (2010). [CrossRef] [PubMed]
  13. J. B. Tenenbaum, V. de Silva, and J. C. Langford, “A global geometric framework for nonlinear dimensionality reduction,” Science290, 2319–2323 (2000). [CrossRef] [PubMed]
  14. S. T. Roweis and S. K. Saul, “Nonlinear dimensionality reduction by locally linear embedding,” Science290, 2323–2326 (2000). [CrossRef] [PubMed]
  15. M. Belkin and P. Niyogi, “Laplacian eigenmaps for dimensionality reduction and data representation,” Neural Comput.13, 1373–1396 (2003). [CrossRef]
  16. D. L. Donoho and C. Grimes, “Hessian eigenmaps: New locally linear embedding techniques for high-dimensional data,” Proc. Natl. Acad. Sci.100, 5591–5596 (2003). [CrossRef]
  17. R. R. Coifman, S. Lafon, A. B. Lee, M. Maggioni, B. Nadler, F. Warner, and S. Zucker, “Geometric diffusions as a tool for harmonic analysis and structure definition on data,” Proc. Natl. Acad. Sci.102, 7426–7431 (2005). [CrossRef] [PubMed]
  18. R. R. Coifman and S. Lafon, “Diffusion maps,” Appl. Comput. Harmon. Anal.21, 5–30 (2006). [CrossRef]
  19. R. R. Coifman, Y. Shkolnisky, F. J. Sigworth, and A. Singer, “Reference free structure determination through eigenvectors of center of mass operators,” Appl. Comput. Harmon. Anal.28, 296–312 (2010). [CrossRef] [PubMed]
  20. C. M. Bishop, M. Svensen, and C. K. I. Williams, “GTM: The generative topographic mapping,” Neural Computation463, 379–383 (1998).
  21. R. R. Coifman, Y. Shkolnisky, F. J. Sigworth, and A. Singer, “Graph Laplacian tomography from unknown random projections,” IEEE Trans. Image Process.17, 1891–1899 (2008). [CrossRef] [PubMed]
  22. A. Singer, R. R. Coifman, F. J. Sigworth, D. W. Chester, and Y. Shkolnisky, “Detecting consistent common lines in cryo-EM by voting,” J. Struct. Biol.169, 312–322 (2010). [CrossRef]
  23. J. Frank, Three-Dimensional Electron Microscopy of Macromolecular Assemblies: Visualization of Biological Molecules in Their Native State (Oxford University Press, 2006). [CrossRef] [PubMed]
  24. A. H. Taub, “Empty space-times admitting a three parameter group of motions,” Ann. Math.53, 472–490 (1951). [CrossRef]
  25. B. L. Hu, “Scalar waves in the mixmaster universe. I. The Helmholtz equation in a fixed background,” Phys. Rev. D8, 1048–1060 (1973). [CrossRef]
  26. L. C. Biedenharn and J. D. Louck, Angular Momentum in Quantum Physics (Addison Wesley, Reading, 1981).
  27. Y. LeCun, J. S. Denker, S. Solla, R. E. Howard, and L. D. Jackel, “Optimal brain damage,” in Advances in Neural Information Processing Systems (NIPS 1989), 2, D. Touretzky, ed. (Morgan Kaufman, Denver, CO, 1990), pp. 598–605.
  28. G. W. Stewart, “Error and perturbation bounds for subspaces associated with certain eigenvalue problems,” SIAM Rev.15, 727–764 (1973). [CrossRef]
  29. L. Lovisolo and E. A. B. da Silva, “Uniform distribution of points on a hyper-sphere with applications to vector bit-plane encoding,” IEEE Proc., Vis. Image Signal Process.148, 187–193 (2001). [CrossRef]
  30. D. T. Cromer and J. B. Mann, “Atomic scattering factors computed from numerical Hartree-Fock wavefunctions,” Acta Cryst. A24, 321–324 (1968). [CrossRef]
  31. D. E. Knuth, The Art of Computer Programming: Seminumerical Algorithms, 3rd ed., (Addison-Wesley, 1997), Vol. 2.
  32. P. Schwander, “Efficient interpolation of scattering data to an arbitrary grid,” (in preparation, 2012).
  33. L. Palatinus and G. Chapuis, “SUPERFLIP – a computer program for the solution of crystal structures by charge flipping in arbitrary dimensions,” J. Appl. Cryst.40, 786–790 (2007). [CrossRef]
  34. B. Moths and A. Ourmazd, “Bayesian algorithms for recovering structure from single-particle diffraction snapshots of unknown orientation: a comparison,” Acta. Cryst.A67, 481–486 (2011).
  35. H. N. Chapman, P. Fromme, A. Barty, T. A. White, R. A. Kirian, A. Aquila, M. S. Hunter, J. Schulz, D. P. De-Ponte, U. Weierstall, R. B. Doak, F. R. N. C. Maia, A. V. Martin, I. Schlichting, L. Lomb, N. Coppola, R. L. Shoeman, S. W. Epp, R. Hartmann, D. Rolles, A. Rudenko, L. Foucar, N. Kimmel, G. Weidenspointner, P. Holl, M. Liang, M. Barthelmess, C. Caleman, S. Boutet, M. J. Bogan, J. Krzywinski, C. Bostedt, S. Bajt, L. Gumprecht, B. Rudek, B. Erk, C. Schmidt, A. Hömke, C. Reich, D. Pietschner, L. Strüder, G. Hauser, H. Gorke, J. Ullrich, S. Herrmann, G. Schaller, F. Schopper, H. Soltau, K. Kühnel, M. Messerschmidt, J. D. Bozek, S. P. Hau-Riege, M. Frank, C. Y. Hampton, R. G. Sierra, D. Starodub, G. J. Williams, J. Hajdu, N. Timneanu, M. M. Seibert, J. Andreasson, A. Rocker, O. Jönsson, M. Svenda, S. Stern, K. Nass, R. Andritschke, C. Schröter, F. Krasniqi, M. Bott, K. E. Schmidt, X. Wang, I. Grotjohann, J. M. Holton, T. R. M. Barends, R. Neutze, S. Marchesini, R. Fromme, S. Schorb, D. Rupp, M. Adolph, T. Gorkhover, I. Andersson, H. Hirsemann, G. Potdevin, H. Graafsma, B. Nilsson, and J. C. H. Spence, “Femtosecond X-ray protein nanocrystallography,” Nature470, 73–77 (2011). [CrossRef] [PubMed]
  36. J. Zhang, M. L. Baker, G. F. Schröder, N. R. Douglas, S. Reissmann, J. Jakana, M. Dougherty, C. J. Fu, M. Levitt, S. J. Ludtke, J. Frydman, and W. Chiu, “Mechanism of folding chamber closure in a group II chaperonin,” Nature463, 379–383 (2010). [CrossRef] [PubMed]
  37. S. J. Ludtke, P. R. Baldwin, and W. Chiu, “EMAN: Semiautomated software for high-resolution single-particle reconstructions,” J. Struct. Biol.128, 82–97 (1999). [CrossRef] [PubMed]
  38. J. Frank and L. Al-Ali, “Signal-to-noise ratio of electron micrographs obtained by cross-correlation,” Nature256, 376–379 (1975). [CrossRef] [PubMed]
  39. J. F. M. Svensen, “GTM: The generative topographic mapping,” Ph.D. thesis, Aston University (1998).
  40. J. Frank, M. Radermacher, P. Penczek, J. Zhu, Y. Li, M. Ladjadj, and A. Leith, “SPIDER and WEB: processing and visualization of images in 3D electron microscopy and related fields,” J. Struct. Biol.116, 190 (1996). [CrossRef] [PubMed]
  41. J M. Glownia, J. Cryan, J. Andreasson, A. Belkacem, N. Berrah, C. I. Blaga, C. Bostedt, J. Bozek, L. F. Di-Mauro, L. Fang, J. Frisch, O. Gessner, M. Gühr, J. Hajdu, M. P. Hertlein, M. Hoener, G. Huang, O. Kornilov, J. P. Marangos, A. M. March, B. K. McFarland, H. Merdji, V. S. Petrovic, C. Raman, D. Ray, D. A. Reis, M. Trigo, J. L. White, W. White, R. Wilcox, L. Young, R. N. Coffee, and P. H. Bucksbaum, “Time-resolved pump-probe experiments at the LCLS,” Opt. Express18, 17620–17630 (2010). [CrossRef] [PubMed]
  42. J. P. Cryan, J. M. Glownia, J. Andreasson, A. Belkacem, N. Berrah, C. I. Blaga, C. Bostedt, J. Bozek, C. Buth, L. F. DiMauro, L. Fang, O. Gessner, M. Guehr, J. Hajdu, M. P. Hertlein, M. Hoener, O. Kornilov, J. P. Marangos, A. M. March, B. K. McFarland, H. Merdji, V. S. Petrović, C. Raman, D. Ray, D. Reis, F. Tarantelli, M. Trigo, J. L. White, W. White, L. Young, P. H. Bucksbaum, and R. N. Coffee, “Auger electron angular distribution of double core-hole states in the molecular reference frame,” Phys. Rev. Lett.105, 083004 (2010). [CrossRef] [PubMed]
  43. M. Balasubramanian and E. L. Schwartz, “The Isomap algorithm and topological stability,” Science295, 5552 (2002). [CrossRef]
  44. B. Zhang, M. J. Fadili, J. L. Starck, and J. C. Olivo-Marin, “Multiscale variance-stabilizing transform for mixed-Poisson-Gaussian processes and its applications in bioimaging,” in Proceedings of IEEE International Conference on Image Processing, 6 (Institute of Electrical and Electronics Engineers, New York), 233–236.
  45. B. Zhang, J. Fadili, and J. Starck, “Wavelets, ridgelets, and curvelets for Poisson noise removal,” IEEE Trans. Image Process.17, 1093–1108 (2008). [CrossRef] [PubMed]
  46. Y. Guan, “Variance stabilizing transformations of Poisson, binomial and negative binomial distributions,” Stat. Probabil. Lett.14, 1621–1629 (2009).
  47. L. Zelnik-Manor and P. Perona, “Self-tuning spectral clustering,” in Advances in neural information processing systems, 17 (2004), 1601–1608.
  48. J. Chen and I. Safro, “Algebraic distance on graphs,” SIAM J. Sci. Comput. (2010). Submitted.
  49. UCSF CHIMERA package, Resource for Biocomputing, Visualization, and Informatics, University of California, San Francisco (supported by NIH P41 RR-01081).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited