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2015 | 3 | 1 |
Tytuł artykułu

Fast and Robust Orientation of Cryo-Electron Microscopy Images

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We present an efficient and reliable algorithm for determining the orientations of noisy images obtained fromprojections of a three-dimensional object. Based on the linear relationship among the common line vectors in one image plane, we construct a sparse matrix, and show that the coordinates of the common line vectors are the eigenvectors of the matrix with respect to the eigenvalue 1. The projection directions and in-plane rotation angles can be determined fromthese coordinates. A robust computation method of common lines in the real space using aweighted cross-correlation function is proposed to increase the robustness of the algorithm against the noise. A small number of good leading images, which have the maximal dissimilarity, are used to increase the reliability of orientations and improve the efficiency for determining the orientations of all the images. Numerical experiments show that the proposed algorithm is effective and efficient.
Wydawca
Rocznik
Tom
3
Numer
1
Opis fizyczny
Daty
otrzymano
2015-08-14
zaakceptowano
2015-10-30
online
2015-11-30
Twórcy
autor
  • LSEC, Institute of Computational Mathematics, Academy of Mathematics and
    System Sciences, Chinese Academy of Sciences, Beijing 100190, China
autor
  • LSEC, Institute of Computational Mathematics, Academy of Mathematics and
    System Sciences, Chinese Academy of Sciences, Beijing 100190, China
autor
  • LSEC, Institute of Computational Mathematics, Academy of Mathematics and
    System Sciences, Chinese Academy of Sciences, Beijing 100190, China
autor
  • LSEC, Institute of Computational Mathematics, Academy of Mathematics and
    System Sciences, Chinese Academy of Sciences, Beijing 100190, China
Bibliografia
  • [1] T. S. Baker. Chen and R. H. Cheng. A Model-Based Approach for Determining Orientations of Biological MacromoleculesImaged by Cryoelectron Microscopy. Journal of Structural Biology, 116(1):120-130, 1996.
  • [2] C. Chen and G. Xu. Gradient-flow-based semi-implicit finite-element method and its convergence analysis for image reconstruction.Inverse Problems, 28(3):035006, 2012.[WoS][Crossref]
  • [3] R. A. Crowther, D. J. DeRosier, and A. Klug. The reconstruction of a three-dimensional structure from projections and itsapplication to electron microscopy. Proceedings of the Royal Society of London. Series A,Mathematical and Physical Sciences,317(1530):319–340, 1970.
  • [4] R. A. Crowther. Procedures for Three-Dimensional Reconstruction of Spherical Viruses by Fourier Synthesis from ElectronMicrographs. Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 261(837):221–228,1971.
  • [5] S. D. Fuller, S. J Butcher, R. H. Cheng, and T. S. Baker. Three-Dimensional Reconstruction of Icosahedral Particles-The UncommonLine. J. Struct. Biol., 116:48–55, 1996.
  • [6] J. Frank. Three-Dimensional ElectronMicroscopy ofMacromolecular Assemblies: Visualization of BiologicalMolecules in TheirNative State. Oxford, 2006.
  • [7] Frank.J.(Ed.). Electron Tomography Methods for Three-dimensional Visualization of Structures in the cell. Springer, New York.
  • [8] G. Golub and C. Van Loan. Matrix Computations. The Johns Hopkins University Press, 1996.
  • [9] A. Gopinath, G. Xu, D. Ress, O. Oktem, S. Subramaniam, and C. Bajaj. Shape-based Regularization of Electron TomographicReconstruction. IEEE Trans Med Imaging, 31(12):2241–2252, 2012.
  • [10] M. Van Heel. Angular reconstitution: a posteriori assignment of projection directions for 3d reconstruction. Ultramicroscopy,21(2):111–124, 1987.[Crossref]
  • [11] M. Li, G. Xu, C. O. S. Sorzano, F. Sun, and C. L. Bajaj. Single-Particle Reconstruction Using L2-Gradient Flow. Journal ofStructural Biology, 176:259–267, 2011.[WoS]
  • [12] S. J. Ludtke, P. R. Baldwin, and W. Chiu. EMAN: semiautomated software for highresolution single-particle reconstructions.Journal of Structural Biology, 128(1):82-97, 1999.
  • [13] F. Natterer. The Mathematics of Computerized Tomography. SIAM: Society for Industrial and Applied Mathematics, 2001.
  • [14] F. Natterer and F. Wübbeling. Mathematical Methods in Image Reconstruction. SIAM, 2001.
  • [15] P. A. Penczek, R. A. Grasucci, and J. Frank. The ribosome at improved resolution: New techniques for merging and orientationrefinement in 3D cryo-electron microscopy of biological particles. Ultramicroscopy, 53:251–270, 1994.
  • [16] L. Piegl and W. Tiller. The NURBS Book. Springer, 1997.
  • [17] M. Radermacher. Three-dimensional reconstruction from random projections–orientational alignment via Radon transforms.Ultramicroscopy, 53:121–136, 1994.
  • [18] M. Radermacher. The three-dimensional reconstruction of single particles from random and non-random tilt series. J.Electron Microsc. Tech., 9:359–394, 1988.[Crossref]
  • [19] P. B. Rosenthal and R. Henderson. Optimal Determination of Particle Orientation, Absolute Hand, and Contrast Loss inSingle-particle Electron Cryomicroscopy. Journal of Molecular Biology, 333(4):721–745, 2003.
  • [20] H. R. Saibil. Macromolecular structure determination by cryo-electron microscopy. Acta Cryst. D, 56:1215–1222, 2000.
  • [21] S. H. W. Scheres. RELION: Implementation of a Bayesian approach to cryo-EM structure determination. J. Struct Biol.,180(3):519–530, 2012.
  • [22] R. R. Coifman, Y. Shkolnisky, F. J. Sigworth, and A. Singer. Reference free structure determination through eigenvectors ofcenter of mass operators. Appl. Comput. Harmon. Anal., 28:296-312, 2010.[WoS]
  • [23] Y. Shkolnisky and A. Singer. Viewing direction estimation in cryo-em using synchronization. SIAM J. Imageing Sciences,5(3):1088–1110, 2012.[WoS]
  • [24] A. Singer and Y. Shkolnisky. Three-dimensional structure determination from common lines in cryo-em by eigenvectors andsemidefinite programming. SIAM J. Imageing Sciences, 4(2):543–572, 2011.[WoS]
  • [25] L. Wang, A. Singer and Z. Wen. Orientation Determination from Cryo-EM images Using Least Unsquared Deviation.http://arxiv.org/pdf/1211.7045v1.
  • [26] C. O. S. Sorzano, S. Jonic, C. El-Bez, J. M. Carazo, S. De Carlo, P. Thévenaz, and M. Unser. A multiresolution approach to poseassignment in 3-D electron microscopy of single particles. J. Struct. Biol., 146:381–392, 2004.
  • [27] X. Wang and G. Xu. A Fast Classification Method for Single-Particle Projections with a Translation and Rotation Invariant.Journal of Comp. Math., 31:2(2013), 137-153.[WoS]
  • [28] G. Xu, M. Li, A. Gopinath, and C. L. Bajaj. Inversion of Electron Tomography Images Using L2-Gradient Flows–ComputationalMethods. Journal of Computational Mathematics, 29(5):501–525, 2011. [WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_mlbmb-2015-0010
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