@inproceedings{ee1d833ed81945a1aa25f72a133f84ba,

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

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.",

author = "Junghoon Lee and Yili Zheng and Doerschuk, {Peter C.}",

year = "2006",

doi = "10.1117/12.659440",

language = "English (US)",

isbn = "0819461059",

series = "Proceedings of SPIE - The International Society for Optical Engineering",

booktitle = "Computational Imaging IV - Proceedings of SPIE-IS and T Electronic Imaging",

note = "Computational Imaging IV ; Conference date: 16-01-2006 Through 18-01-2006",

}