Image restoration in cryo-electron microscopy

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 (EM), 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 EM, 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 EM map that makes it visually comparable to maps determined by X-ray crystallography, and thus amenable to comparative interpretation. Finally, we present a semiheuristic 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.