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 analysis (correspondence analysis, principal components); outlier detection schemes; statistical criteria for the quantitative assessment of spatial resolution (spectral signal-to-noise ratios); and a fast algorithm for the determination of the scaling factors between two micrographs. In order to obtain higher-resolution 3-D reconstructions of icosahedral viruses, a current goal is to combine a larger number of micrographs with slight disparities in magnification and image contrast. One objective, to address the issue of geometric corrections, led us to the development of new algorithms for estimating and performing the required geometrical transformations (scaling, translation, and rotation) with the least amount of distortion (least squares criterion). We are also working on the second deconvolution aspect of the problem, and have developed new multichannel identification and deconvolution techniques that should allow us to correct for the effect of the contrast transfer function of the microscope. These methods require the availability of multiple images of the same specimen recorded at varying degrees of defocus.
