A Wavelet Based Alternative Iteration Method for the Orientation Refinement of Cryo-Electron Microscopy 3D Reconstruction

Abstract

Cryo-electron microscopy (cryo-EM) single particle method (SPM) reconstructs the three-dimensional (3D) density map of biological macromolecules using 2D particle images with estimated orientations. The estimated orientations have errors which result in the decrease in resolution of the reconstructed map. We propose a wavelet orthonormal bases based iteration method by refining alternatively the orientations and the map using Levenberg{Marquardt algorithm and soft-thresholding, respectively. The convergence analysis of the proposed algorithm is provided and numerical experiments for simulated particle images show its good performance.

Keywords:

• alternating-direction method
• convergence analysis
• inverse problem
• nonlinear least squares
• Haar wavelet

AMS Subject Classification:

• 68U10
• 65J22
• 65T60
• 94A08
• 90C90