A fast algorithm for 3-D reconstruction from unoriented projections and cryo electron microscopy of viruses

Junghoon Lee, Yili Zheng, Peter C. Doerschuk

Research output: Chapter in Book/Report/Conference proceedingConference contribution


In a cryo electron microscopy experiment, the data is noisy 2-D projection images of the 3-D electron scattering intensity where the orientation of the projections is not known. In previous work we have developed a solution for this problem based on a maximum likelihood estimator that is computed by an expectation maximization algorithm. In the expectation maximization algorithm the expensive step is the expectation which requires numerical evaluation of 3- or 5-dimensional integrations of a square matrix of dimension equal to the number of Fourier series coefficients used to describe the 3-D reconstruction. By taking advantage of the rotational properties of spherical harmonics, we can reduce the integrations of a matrix to integrations of a scalar. The key properties is that a rotated spherical harmonic can be expressed as a linear combination of the other harmonics of the same order and that the weights in the linear combination factor so that each of the three factors is a function of only one of the Euler angles describing the orientation of the projection.

Original languageEnglish (US)
Title of host publicationComputational Imaging IV - Proceedings of SPIE-IS and T Electronic Imaging
StatePublished - 2006
Externally publishedYes
EventComputational Imaging IV - San Jose, CA, United States
Duration: Jan 16 2006Jan 18 2006

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


OtherComputational Imaging IV
Country/TerritoryUnited States
CitySan Jose, CA

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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