Alignment, classification, and three-dimensional reconstruction of single particles embedded in ice.

Cryo-electron microscopy of single biological particles poses new challenges to digital image processing due to the low signal-to-noise ratio of the data. New tools have been devised to deal with important aspects of 3-D reconstruction following the random-conical data collection scheme: (a) a new shift-invariant function has been derived, which promises to facilitate alignment and classification of single particle projections; (b) a new method of orientation search is proposed, which makes it possible to relate random-conical data sets to one another prior to reconstruction; and (c) the foundation is laid for a 3-D variance estimation which utilizes the oversampling of 3-D angular space by projections in the random-conical reconstruction scheme.