Computing the 3-D structure of viruses from unoriented cryo electron microscope images: a fast algorithm for a statistical approach.
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.
Lee
Junghoon
J
Sch. of Electr. & Comput. Eng., Purdue Univ., West Lafayette, IN 47907, USA. junghoon@purdue.edu
Zheng
Yili
Y
Doerschuk
Peter C
PC
D000465:Algorithms; D001185:Artificial Intelligence; D002213:Capsid / Q000648:ultrastructure*; D020285:Cryoelectron Microscopy / Q000379:methods*; D003627:Data Interpretation, Statistical; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D013997:Time Factors