  Cryo-electron microscopy (EM) single particle reconstruction is an entirely
general technique for 3D structure determination of macromolecular complexes.
However, because the images are taken at low electron dose, it is extremely
hard to visualize the individual particle with low contrast and high noise
level. In this paper, we propose a novel approach called multi-frequency vector
diffusion maps (MFVDM) to improve the efficiency and accuracy of cryo-EM 2D
image classification and denoising. This framework incorporates different
irreducible representations of the estimated alignment between similar images.
In addition, we propose a graph filtering scheme to denoise the images using
the eigenvalues and eigenvectors of the MFVDM matrices. Through both simulated
and publicly available real data, we demonstrate that our proposed method is
efficient and robust to noise compared with the state-of-the-art cryo-EM 2D
class averaging and image restoration algorithms.
