2 February 2006 A fast algorithm for 3D reconstruction from unoriented projections and cryo electron microscopy of viruses
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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 coeffcients 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.
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Junghoon Lee, Junghoon Lee, Yili Zheng, Yili Zheng, Peter C. Doerschuk, Peter C. Doerschuk, } "A fast algorithm for 3D reconstruction from unoriented projections and cryo electron microscopy of viruses", Proc. SPIE 6065, Computational Imaging IV, 60650A (2 February 2006); doi: 10.1117/12.659440; https://doi.org/10.1117/12.659440
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