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Computing the 3-D structure of viruses from unoriented cryo electron microscope images: a fast algorithm for a statistical approach

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3 Author(s)
Junghoon Lee ; Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN ; Yili Zheng ; Doerschuk, P.C.

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

Published in:

Engineering in Medicine and Biology Society, 2006. EMBS '06. 28th Annual International Conference of the IEEE

Date of Conference:

Aug. 30 2006-Sept. 3 2006