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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