### 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 | Proceedings of SPIE - The International Society for Optical Engineering |

Volume | 6065 |

DOIs | |

Publication status | Published - 2006 |

Externally published | Yes |

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

### Other

Other | Computational Imaging IV |
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Country | United States |

City | San Jose, CA |

Period | 1/16/06 → 1/18/06 |

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### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Condensed Matter Physics

### Cite this

*Proceedings of SPIE - The International Society for Optical Engineering*(Vol. 6065). [60650A] https://doi.org/10.1117/12.659440