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. Introduction.In the past few decades, with the advances in specimen preparation methods and image processing techniques, electron microscopy (EM) techniques [14,17,23,24,50,29] have become indispensable tools for determining the three-dimensional (3D) structures of macromolecules, macromolecular complexes, and cells. Among all computerized techniques used in EM, the single particle method (SPM) and electron tomography (ET) are two of the most popular ones. The specimen preparation methods mainly include the negative staining method, in which specimens are stained in heavy metal salts, and the frozen-hydrated method, in which specimens are embedded in vitreous ice. The EM technique using ice-embedded specimens is often called cryo-EM. SPM includes a set of image processing techniques for building up the 3D structure of a particle by using two-dimensional (2D) digitized EM images (projections) of many identical particles. The main modules in the SPM include image alignment and classification; image filtering and contrast transfer function (CTF) correction; and 3D reconstruction (see [24,50,30,29] for more details). These modules are integrated in an iterative framework to iteratively refine the 3D result using the projection matching methods [41]. ET is a tomography technique to reconstruct a detailed 3D structure of the macromolecular complex or cell from 2D images collected from different tilted stages of the object. The main image

Duality for Frames

“…Wavelet frame related algorithms have been developed to solve medical and biological image processing problems, e.g. medical image segmentation [44,113], X-ray computer tomography (CT) image reconstruction [47], and protein molecule 3D reconstruction from electron microscopy images [83]. Frames provide large flexibility in designing filters with improved performance in applications.…”

Development of a fast electromagnetic beam blanker for compressed sensing in scanning transmission electron microscopy

“…In order to discriminate shutter imperfections from reconstruction issues, we compare the reconstructed images with the reconstructions obtained from a virtually shuttered image obtained by applying a digital mask on the unshuttered experimental HAADF image as was typically done in papers discussing compressive sensing so far 13,14,25 . The results are shown in Figure 5, together with the reconstructed experimental images.…”

“…In order to overcome this issue, a wide range of different approaches are being tested in the TEM community like reduction of the kinetic energy of the fast electrons [1][2][3] , improving the detection efficiency of cameras [4][5][6][7] , time resolved approaches [8][9][10] and many more. Relatively recently, the concept of compressive sensing was proposed to significantly reduce the electron dose while maintaining all the important features in a TEM or Scanning TEM (STEM) image [11][12][13][14] . Compressive sensing is based on the assumption that an image contains a significant amount of redundancy and not all pixels in the image are independent.…”

Adaptive frame-based color image denoising

“…The iterative scheme (4.1) has been applied to many image restoration problems in [4,6,7,10,13,17,21] and many references therein.…”