Background: Three-dimensional (3D) reconstruction in single-particle cryo-electron microscopy is a significant technique for recovering the 3D structure of proteins or other biological macromolecules from their two-dimensional (2D) noisy projection images taken from unknown random directions. Class averaging in single-particle cryo-electron microscopy is an important procedure for producing high-quality initial 3D models due to the existence of a high level of noise in the projection images. Image alignment is a fundamental step in the class averaging.
Results: In this paper, an efficient image alignment algorithm using 2D interpolation in the frequency domain of images is proposed to improve the estimation accuracy of alignment parameters. The proposed algorithm firstly uses the Fourier transform of two projection images to calculate a discrete cross-correlation matrix and then performs the 2D interpolation around the maximum value in the cross-correlation matrix. The alignment parameters of rotation angles and translational shifts in the x-axis and y-axis directions between the two projection images are directly determined according to the position of the maximum value in the cross-correlation matrix after interpolation. Furthermore, the proposed algorithm and the K-medoids clustering algorithm are used to compute class averages for single-particle 3D reconstruction.
Conclusions: Results on simulated data set show that the proposed algorithm can be used to compute the alignment parameters efficiently, and using the 2D interpolation can improve the estimation accuracy of the alignment parameters, which usually leads to a better 3D reconstruction result.