### 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 property is that a rotated spherical harmonic can be expressed as a linear combination of the other harmonics of the same order and 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. Numerical example of the reconstructions is provided based on Nudaurelia Omega Capensis Virus.

Original language | English (US) |
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Title of host publication | 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06 |

Pages | 2538-2541 |

Number of pages | 4 |

DOIs | |

State | Published - Dec 1 2006 |

Externally published | Yes |

Event | 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06 - New York, NY, United States Duration: Aug 30 2006 → Sep 3 2006 |

### Publication series

Name | Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings |
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ISSN (Print) | 0589-1019 |

### Other

Other | 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06 |
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Country | United States |

City | New York, NY |

Period | 8/30/06 → 9/3/06 |

### Fingerprint

### ASJC Scopus subject areas

- Signal Processing
- Biomedical Engineering
- Computer Vision and Pattern Recognition
- Health Informatics

### Cite this

*28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06*(pp. 2538-2541). [4029009] (Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings). https://doi.org/10.1109/IEMBS.2006.260210