Image Restoration in Cryo-Electron Microscopy

Abstract

Image restoration techniques are used to obtain, given experimental measurements, the best possible approximation of the original object within the limits imposed by instrumental conditions and noise level in the data. In molecular electron microscopy, we are mainly interested in linear methods that preserve the respective relationships between mass densities within the restored map. Here, we describe the methodology of image restoration in structural electron microscopy, and more specifically, we will focus on the problem of the optimum recovery of Fourier amplitudes given electron microscope data collected under various defocus settings. We discuss in detail two classes of commonly used linear methods, the first of which consists of methods based on pseudoinverse restoration, and which is further subdivided into mean-square error, chi-square error, and constrained based restorations, where the methods in the latter two subclasses explicitly incorporates non-white distribution of noise in the data. The second class of methods is based on the Wiener filtration approach. We show that the Wiener filter-based methodology can be used to obtain a solution to the problem of amplitude correction (or “sharpening”) of the electron microscopy map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparable interpretation. Finally, we present a semi-heuristic Wiener filter-based solution to the problem of image restoration given sets of heterogeneous solutions. We conclude the chapter with a discussion of image restoration protocols implemented in commonly used single particle software packages.

Cryogenic Electron Microscopy and Single-Particle Analysis

“…Although underfocused imaging conditions have to be used, much of the high-resolution information can be recovered computationally (44)(45)(46). Transmission electron microscope images of thin specimens are best described as projection images.…”

PRIME: Probabilistic Initial 3D Model Generation for Single-Particle Cryo-Electron Microscopy

“…CTF correction by phase flipping only corrects the resolution-dependent CTF phase inversions, disregarding the damping of Fourier amplitudes with increasing resolution. Phase-flipped images are noisier than images corrected with more accurate approaches, such as the reciprocal space adaptive Wiener filter (Penczek, 2010). Here, we are concerned with the problem of reconstructing accurate low-resolution maps ab initio from very noisy images.…”

Electron tomography of cells

“…CTF correction can be done for individual 2D images by fitting power spectra to theoretical models (Penczek, 2010b). CTF correction has enabled near-atomic resolution reconstructions of both 2D crystals (Henderson et al 1990) and various ' single ' particles (Bottcher et al 1997 ;Conway et al 1997), but it is challenging in electron tomography because the images are so low contrast and exhibit a defocus gradient.…”