Algorithms for Three-dimensional Reconstruction From the Imperfect Projection Data Provided by Electron Microscopy

  • Jose-Maria Carazo
  • Gabor T. Herman
  • Carlos O. S. Sorzano
  • Roberto Marabini


Since the 1970s, it has become increasingly evident that transmission electron microscopy (TEM) images of typical thin biological specimens carry a large amount of information on 3D macromolecular structure. It has been shown many times how the information contained in a set of TEM images (2D signals) can determine a useful estimate of the 3D structure under study.


Projection Image Fourier Space Projection Direction Algebraic Reconstruction Technique Optical Transfer Function 
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  1. Bilbao-Castro, J. R., Sorzano, C. O. S., García, I. and Fernández, J. J. (2004). Phan3D: design of biological phantoms in 3D electron microscopy. Bioinformatics 20:3286–3288.PubMedCrossRefGoogle Scholar
  2. Censor, Y. and Zenios, S. A. (1997). Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, New York.Google Scholar
  3. Chalcroft, J. P. and Davey, C. L. (1984). A simply constructed extreme-tilt holder for the Philips eucentric stage. J. Microsc. 134:41–48.Google Scholar
  4. Crowther, R. A., DeRosier, D. J. and Klug, F. R. S. (1970). The reconstruction of a threedimensional structure from projections and its application to electron microscopy. Proc. R. Soc.A 317:310–340.CrossRefGoogle Scholar
  5. DeRosier, D. J. and Moore, P.B. (1970). Reconstruction of three-dimensional images from electron micrographs of structures with helical symmetry. J. Mol. Biol. 52:355–369.PubMedCrossRefGoogle Scholar
  6. Ditzel, L., Lowe, J., Stock, D., Stetter, K. O., Huber, H., Huber, R. and Steinbacher, S. (1998). Crystal structure of the thermosome, the archaeal chaperonin and homolog of CCT. Cell 93:125–138.PubMedCrossRefGoogle Scholar
  7. Eggermont, P. P. B., Herman, G. T. and Lent, A. (1981). Iterative algorithms for large partitioned linear systems with applications to image reconstruction. Linear Algebra Appl. 40:37–67.CrossRefGoogle Scholar
  8. Erickson, H. P. and Klug, A. (1971). Measurement and compensation of defocusing and aberrations by Fourier processing of electron micrographs. Philos. Trans. R. Soc. B 261:105–118.CrossRefGoogle Scholar
  9. Fernández, J., Lawrence, A., Roca, J., García, I., Ellisman, M. and Carazo, J. (2002). High performance electron tomography of complex biological specimens. J. Struct. Biol. 138:6–20PubMedCrossRefGoogle Scholar
  10. Furuie, S. S., Herman, G. T., Narayan, T. K., Kinahan, P. E., Karp, J. S., Lewitt, R. M. and Matej, S. (1994). A methodology for testing for statistically significant differences between fully 3D PET reconstruction algorithms. Phys. Med. Biol. 39:341–354.PubMedCrossRefGoogle Scholar
  11. Garduño, E. and Herman, G. T. (2004). Optimization of basis functions for both reconstruction and visualization. Discrete Appl. Math. 139:95–112.CrossRefGoogle Scholar
  12. Herman, G. T. (1980). Image Reconstruction from Projections: The Fundamentals of Computerized Tomography. Academic Press, New York.Google Scholar
  13. Herman, G. T. and Meyer, L. B. (1993). Algebraic reconstruction techniques can be made computationally efficient. IEEE Trans. Medical Imaging 12:600–609.CrossRefGoogle Scholar
  14. Lewitt, R. M. (1990). Multidimensional digital image representations using generalized Kaiser—Bessel window functions. J. Optic. Soc. Am.A 7:1834–1846.CrossRefGoogle Scholar
  15. Lewitt, R. M. (1992). Alternatives to voxels for image representation in iterative reconstruction algorithms. Phys. Med. Biol. 37:705–716.PubMedCrossRefGoogle Scholar
  16. Marabini, R., Herman, G.T. and Carazo, J.M. (1998). 3D reconstruction in electron microscopy using ART with smooth spherically symmetric volume elements (blobs). Ultramicroscopy 72:53–65.PubMedCrossRefGoogle Scholar
  17. Marabini, R., Rietzel, E., Schröder, R., Herman, G. T. and Carazo, J. M. (1997). Three dimensional reconstruction from reduced sets of very noisy images acquired following a singleaxis tilt schema: application of a new three-dimensional reconstruction algorithm and objective comparison with weighted backprojection. J. Struct. Biol. 120:363–371.PubMedCrossRefGoogle Scholar
  18. Matej, S., Herman, G. T., Narayan, T. K., Furuie, S. S., Lewitt, R. M. and Kinahan, P. E. (1994). Evaluation of task-oriented performance of several fully 3D PET reconstruction algorithms. Phys. Med. Biol. 39:355–367.PubMedCrossRefGoogle Scholar
  19. Matej, S. and Lewitt, R. M. (1995). Efficient 3D grids for image reconstruction using spherically-symmetric volume elements. IEEE Trans. Nucl. Sci. 42:1361–1370.CrossRefGoogle Scholar
  20. Matej, S. and Lewitt, R. M. (1996). Practical considerations for 3-D image reconstruction using spherically symmetric volume elements. IEEE Trans. Med. Imaging 15:68–78.PubMedCrossRefGoogle Scholar
  21. Natterer, F. and Wübbeling, F. (2001). Mathematical Methods in Image Reconstruction. SIAM, Philadelphia.Google Scholar
  22. Petersen, D. P. and Middleton, D. (1962). Sampling and reconstruction of wavenumber limited functions in n-dimensional Euclidean spaces. Inform. Control 5:279–323.CrossRefGoogle Scholar
  23. Radermacher, M. (1980). Dreidimensionale Rekonstruktion bei kegelförmiger Kippung im Electronenmikroskop. PhD Thesis, Technische Universität München.Google Scholar
  24. Radermacher, M. (1988). Three-dimensional reconstruction of single particles from random and nonrandom tilt series. J. Electron Microsc. Tech. 9:359–394.PubMedCrossRefGoogle Scholar
  25. Radermacher, M., Wagenknecht, T., Verschoor, A. and Frank, J. (1987). Three-dimensional reconstruction from a single-exposure, random conical tilt series applied to the 50S ribosomal unit. J. Microsc. 146:113–136.PubMedGoogle Scholar
  26. Radon, J. (1917). Über die Bestimmung von Funktionen durch ihre Integralwerte längs gewisser Mannigfaltigkeiten. Berichte über die Verhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig. Math. Phys. Klasse 69:262–277.Google Scholar
  27. Rowland, S. (1979). Computer implementation of image reconstruction formulas. In Image Reconstruction from Projections (G. Herman, ed.). Springer-Verlag, Berlin, pp. 29–79.Google Scholar
  28. Scheres, S.H.W., Valle, M., Núñez, R., Sorzano, C.O.S., Marabini, R., Herman, G.T. and Carazo, J. M. (2005). Maximum-likelihood multi-reference refinement for electron microscopy images. J. Mol. Biol. 348:139–149.PubMedCrossRefGoogle Scholar
  29. Sorzano, C.O.S., Marabini, R., Boisset, N., Rietzel, E., Schröder, R., Herman, G.T. and Carazo, J. M. (2001). The effect of overabundant projection directions on 3D reconstruction algorithms. J. Struct. Biol. 133:108–118.PubMedCrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Jose-Maria Carazo
    • 1
  • Gabor T. Herman
    • 2
  • Carlos O. S. Sorzano
    • 3
  • Roberto Marabini
    • 4
  1. 1.Centro Nacional de Biotecnología (CSIC)Universidad AutónomaCantoblanco, MadridSpain
  2. 2.Department of Computer Science, The Graduate CenterCity University of New YorkNew YorkUSA
  3. 3.Escuela Politécnica SuperiorUniversidad San Pablo-CEUBoadilla del Monte, MadridSpain
  4. 4.Escuela Politécnica SuperiorUniversidad AutónomaCantoblanco, MadridSpain

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