High resolution micrographs are often of poor quality, due to a variety of distortions and, especially, a very low signal-to-noise ratio. For micrographs of quasi-periodic arrays or sets of images of ostensibly identical free-standing particles, visual quality can be improved significantly by using correlation-averaging techniques. Over the years, we have developed several computational techniques for the statistical analysis of sets of electron micrographs of biological macromolecules. These methods include various types of factorial analyses (correspondence analysis, principal components), an outlier detection scheme, clustering algorithms, as well as a statistical criterion for quantitative assessment of spatial resolution (spectral signal-to-noise ratio). An aspect that has been considered in more detail is the possibility of improving signal extraction through the use of weighted averaging techniques. In particular, we have developed a new procedure that computes optimal weights by maximizing a global signal-to-noise ratio criterion. By relating our new averaging procedure with the well known principal component decomposition, we have been able to provide an explanation for the striking similarity that can be observed experimentally between the first eigen-image of a data set and the conventional ensemble average.
