On cross-correlations, averages and noise in electron microscopy

Abstract

The influence of noise on cross-correlations is revisited. Equations are provided describing the influence of noise on the cross-correlations between single images and averaged images and on those between averaged images.

Abstract

Biological samples are radiation-sensitive and require imaging under low-dose conditions to minimize damage. As a result, images contain a high level of noise and exhibit signal-to-noise ratios that are typically significantly smaller than 1. Averaging techniques, either implicit or explicit, are used to overcome the limitations imposed by the high level of noise. Averaging of 2D images showing the same molecule in the same orientation results in highly significant projections. A high-resolution structure can be obtained by combining the information from many single-particle images to determine a 3D structure. Similarly, averaging of multiple copies of macromolecular assembly subvolumes extracted from tomographic reconstructions can lead to a virtually noise-free high-resolution structure. Cross-correlation methods are often used in the alignment and classification steps of averaging processes for both 2D images and 3D volumes. However, the high noise level can bias alignment and certain classification results. While other approaches may be implicitly affected, sensitivity to noise is most apparent in multireference alignments, 3D reference-based projection alignments and projection-based volume alignments. Here, the influence of the image signal-to-noise ratio on the value of the cross-correlation coefficient is analyzed and a method for compensating for this effect is provided.