Wavelet Frame Based Algorithm for 3D Reconstruction in Electron Microscopy

Abstract

In electron microscopy, three-dimensional (3D) reconstruction is one key component in many computerized techniques for solving 3D structures of large protein assemblies using electron microscopy images of particles. Main challenges in 3D reconstruction include very low signal-to-noise ratio and very large scale of data sets involved in the computation. Motivated by the recent advances of sparsity-based regularization in the wavelet frame domain for solving various linear inverse problems in imaging science, we proposed a wavelet tight frame based 3D reconstruction approach that exploits the sparsity of the 3D density map in a wavelet tight frame system. The proposed approach not only runs efficiently in terms of CPU time but also requires a much lower memory footprint than existing framelet-based regularization methods. The convergence of the proposed iterative scheme and the functional it minimizes is also examined, together with the connection to existing wavelet frame based regularizations. The numerical experiments showed good performance of the proposed method when it is used in two electron microscopy techniques: the single particle method and electron tomography.