### Abstract

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 language | English (US) |
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Title of host publication | Computational Imaging IV - Proceedings of SPIE-IS and T Electronic Imaging |

DOIs | |

State | Published - Apr 17 2006 |

Externally published | Yes |

Event | Computational Imaging IV - San Jose, CA, United States Duration: Jan 16 2006 → Jan 18 2006 |

### Publication series

Name | Proceedings of SPIE - The International Society for Optical Engineering |
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Volume | 6065 |

ISSN (Print) | 0277-786X |

### Other

Other | Computational Imaging IV |
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Country | United States |

City | San Jose, CA |

Period | 1/16/06 → 1/18/06 |

### 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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## Cite this

*Computational Imaging IV - Proceedings of SPIE-IS and T Electronic Imaging*[60650A] (Proceedings of SPIE - The International Society for Optical Engineering; Vol. 6065). https://doi.org/10.1117/12.659440