TY - GEN
T1 - Computing the 3-D structure of viruses from unoriented cryo electron microscope images
T2 - 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06
AU - Lee, Junghoon
AU - Zheng, Yili
AU - Doerschuk, Peter C.
PY - 2006
Y1 - 2006
N2 - 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.
AB - 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.
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U2 - 10.1109/IEMBS.2006.260210
DO - 10.1109/IEMBS.2006.260210
M3 - Conference contribution
C2 - 17945721
AN - SCOPUS:34047127577
SN - 1424400325
SN - 9781424400324
T3 - Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings
SP - 2538
EP - 2541
BT - 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06
Y2 - 30 August 2006 through 3 September 2006
ER -