Exact reduced-complexity maximum likelihood reconstruction of multiple 3-D objects from unlabeled unoriented 2-D projections and electron microscopy of viruses

Junghoon Lee, Peter C. Doerschuk, John E. Johnson

Research output: Contribution to journalArticle

Abstract

In cryo-electron microscopy, the data is comprised of noisy 2-D projection images of the 3-D electron scattering intensity of the object where the orientation of the projections is unknown. Often, the images show randomly selected objects from a mixture of different types of objects. Objects of different type may be unrelated, e.g., different species of virus, or related, e.g., different conformations of the same species of virus. Due to the low SNR and the 2-D nature of the data, it is challenging to determine the type of the object shown in an individual image. A statistical model and maximum likelihood estimator that computes simultaneous 3-D reconstruction and labels using an expectation maximization algorithm exists but requires extensive computation due to the numerical evaluation of 3-D or 5-D integrations of a square matrix of dimension equal to the number of degrees of freedom in the 3-D reconstruction. By exploiting the geometry of rotations in 3-D, the estimation problem can be transformed so that the inner-most numerical integral has a scalar rather than a matrix integrand. This leads to a dramatic reduction in computation, especially as the number of degrees of freedom in the 3-D reconstruction increases. Numerical examples of the 3-D reconstructions are provided based on synthetic and experimental images where the objects are small spherical viruses.

Original languageEnglish (US)
Pages (from-to)2865-2878
Number of pages14
JournalIEEE Transactions on Image Processing
Volume16
Issue number12
DOIs
StatePublished - Dec 2007
Externally publishedYes

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Electron Microscopy
Viruses
Electron microscopy
Maximum likelihood
Virus
3D
Maximum Likelihood
3D Reconstruction
Projection
Electron scattering
Conformations
Labels
Degree of freedom
Geometry
Expectation-maximization Algorithm
Square matrix
Integrand
Conformation
Maximum Likelihood Estimator
Statistical Model

Keywords

  • 3-D signal reconstruction
  • Cryo-electron microscopy (cryo EM)
  • Expectation maximization algorithm
  • Maximum likelihood estimation
  • Structural biology
  • Tomography
  • Virology
  • Virus

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

Cite this

Exact reduced-complexity maximum likelihood reconstruction of multiple 3-D objects from unlabeled unoriented 2-D projections and electron microscopy of viruses. / Lee, Junghoon; Doerschuk, Peter C.; Johnson, John E.

In: IEEE Transactions on Image Processing, Vol. 16, No. 12, 12.2007, p. 2865-2878.

Research output: Contribution to journalArticle

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