Advertisement

Reconstruction from Microscopic Projections with Defocus-Gradient and Attenuation Effects

Chapter
Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Abstract

We discuss and illustrate defocus-gradient and attenuation effects that are part of the image formation models of microscopy of biological specimens. We demonstrate how they affect the projection data and in turn the 3D reconstructions. Biologically meaningful results can be obtained ignoring both of these effects, but using image processing techniques to incorporate corrections for them into reconstruction methods provides more accurate reconstructions, with potential for creating higher-resolution models of the biological specimens.

Keywords

Reconstruction Method Projection Data Projection Image Attenuation Effect Forward Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

The work presented here is currently supported by the National Science Foundation award number DMS-1114901.

The authors would like to thank Joaquín Otón, José-María Carazo, Carlos Óscar Sánchez Sorzano, and Roberto Marabini for helpful discussions on microscopy and Roberto Marabini and Joachim Frank for comments on this manuscript.

References

  1. 1.
    Attwood D (2007) Soft X-Rays and extreme ultraviolet radiation: Principles and applications. Cambridge University Press, New YorkGoogle Scholar
  2. 2.
    Censor Y, Elfving T, Herman GT (1985) A method of iterative data refinement and its applications. Math Meth Appl Sci 7:108–123CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Eibauer M, Hoffmann C, Plitzko JM, Baumeister W, Nickell S, Engelhardt H (2012) Unraveling the structure of membrane proteins in situ by transfer function corrected cryo-electron tomography. J Struct Biol 180:488–496CrossRefGoogle Scholar
  4. 4.
    Falcone R, Jacobsen C, Kirz J, Marchesini S, Shapiro D, Spence J (2011) New directions in X-ray microscopy. Contemp Phys 52:293–318CrossRefGoogle Scholar
  5. 5.
    Fernandez JJ, Li S, Crowther RA (2006a) CTF determination and correction in electron cryotomography. Ultramicroscopy 106:587–596CrossRefGoogle Scholar
  6. 6.
    Fernandez JJ, Sarzano COS, Marabini R, Carazo JM (2006b) Image processing and 3-D reconstruction in electron microscopy. IEEE Signal Process Mag 23(3):84–94CrossRefGoogle Scholar
  7. 7.
    Frank J (2006) Three-dimensional electron microscopy of macromolecular assemblies, 2nd edn. Oxford University PressGoogle Scholar
  8. 8.
    Herman GT (2009) Fundamentals of computerized tomography: Image reconstruction from projections, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  9. 9.
    Howells M, Jacobsen C, Warwick T, Bos A (2007) Principles and applications of zone plate X-ray microscopes. In: Hawkes P, Spence J (eds) Science of microscopy, Springer, New York pp 835–926CrossRefGoogle Scholar
  10. 10.
    Jensen GJ, Briegel A (2007) How electron cryotomography is opening a new window onto prokaryotic ultrastructure. Curr Opin Struc Biol 17:260–267CrossRefGoogle Scholar
  11. 11.
    Jensen GJ, Kornberg RD (2000) Defocus-gradient corrected back-projection. Ultramicroscopy 84:57–64CrossRefGoogle Scholar
  12. 12.
    Kazantsev IG, Klukowska J, Herman GT, Cernetic L (2010) Fully three-dimensional defocus-gradient corrected backprojection in cryoelectron microscopy. Ultramicroscopy 110:1128–42CrossRefGoogle Scholar
  13. 13.
    Klukowska J, Davidi R, Herman GT (2013) SNARK09 - a software package for reconstruction of 2D images from 1D projections. Comput Methods Programs Biomed 110:424–440CrossRefGoogle Scholar
  14. 14.
    Leis AP, Beck M, Gruska M, Best C, Hegerl R, Baumeister W, Leis JW (2006) Cryo-electron tomography of biological specimens. IEEE Signal Process Mag 23(3):95–103CrossRefGoogle Scholar
  15. 15.
    McDermott G, Le Gros M, Knoechel CG, Uchida M, Larabell CA (2009) Soft X-ray tomography and cryogenic light microscopy: The cool combination in cellular imaging. Trends Cell Biol 19:587–595CrossRefGoogle Scholar
  16. 16.
    Midgley PA, Ward EPW, Hungría AB, Thomas JM (2007) Nanotomography in the chemical, biological and materials sciences. Chem Soc Rev 36:1477–1494CrossRefGoogle Scholar
  17. 17.
    Müller WG, Heymann JB, Nagashima K, Guttmann P, Werner S, Rehbein S, Schneider G, McNally JG (2012) Towards an atlas of mammalian cell ultrastructure by cryo soft X-ray tomography. J Struct Biol 177:179–192CrossRefGoogle Scholar
  18. 18.
    Natterer F, Wübbeling F (2001) Mathematical methods in image reconstruction. Society for Industrial and Applied Mathematics. PhiladelphiaGoogle Scholar
  19. 19.
    Oton J, Sorzano COS, Pereiro E, Cuenca-Alba J, Navarro R, Carazo JM, Marabini R (2012) Image formation in cellular X-ray microscopy. J Struct Biol 178:29–37CrossRefGoogle Scholar
  20. 20.
    Oton J, Sorzano COS, Chichon FJ, Carrascosa JL, Carazo JM, Marabini R (2013) Soft X-ray tomography imaging for biological samples. In: Herman GT, Frank J (eds) Computational Methods for Three-Dimensional Microscopy Reconstruction, Springer 187–220Google Scholar
  21. 21.
    Philippsen A, Engel HA, Engel A (2007) The contrast-imaging function for tilted specimens. Ultramicroscopy 107:202–212CrossRefGoogle Scholar
  22. 22.
    Reimer L, Kohl H (2008) Transmission electron microscopy: Physics of image formation. Springer, New YorkGoogle Scholar
  23. 23.
    Rosenfeld A, Kak AC (1982) Digital picture processing, vol 1, 2nd edn. Academic Press, New YorkGoogle Scholar
  24. 24.
    Rowland SW (1979) Computer implementation of image reconstruction formulas. In: Herman GT (ed) Image reconstruction from projections: Implementation and applications, Springer-Verlag Berlin Heildelberg, pp 9–79Google Scholar
  25. 25.
    Sorzano COS, Marabini R, Herman GT, Censor Y, Carazo JM (2004) Transfer function restoration in 3D electron microscopy via iterative data refinement. Phys Med Biol 49: 509–522CrossRefGoogle Scholar
  26. 26.
    Voortman LM, Stallinga S, Schoenmakers RHM, van Vliet L, Rieger B (2011) A fast algorithm for computing and correcting the CTF for tilted, thick specimens in TEM. Ultramicroscopy 111:1029–1036CrossRefGoogle Scholar
  27. 27.
    Voortman LM, Franken EM, van Vliet LJ, Rieger B (2012) Fast, spatially varying CTF correction in TEM. Ultramicroscopy 118:26–34CrossRefGoogle Scholar
  28. 28.
    Weiss D, Schneider G, Niemann B, Guttmann P, Rudolph D, Schmahl G (2000) Computed tomography of cryogenic biological specimens based on X-ray microscopic images. Ultramicroscopy 84:185–197CrossRefGoogle Scholar
  29. 29.
    Winkler H, Taylor KA (2003) Focus gradient correction applied to tilt series image data used in electron tomography. J Struct Biol 143:24–32CrossRefGoogle Scholar
  30. 30.
    Zanetti G, Riches JD, Fuller SD, Briggs JAG (2009) Contrast transfer function correction applied to cryo-electron tomography and sub-tomogram averaging. J Struct Biol 168:305–312CrossRefGoogle Scholar
  31. 31.
    Zubelli JP, Marabini R, Sorzano COS, Herman GT (2003) Reconstruction by Chahine’s method from electron microscopic projections corrupted by instrumental aberrations. Inverse Probl 19:933–949CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Computer Science, The Graduate CenterCity University of New YorkNew YorkUSA

Personalised recommendations