Three-dimensional reconstruction from random projections: orientational alignment via Radon transforms.

A method for alignment of projections with unknown projecting directions towards a three-dimensional reference has been developed. The technique has been applied to the three-dimensional reconstruction from images of a frozen-hydrated preparation of 50S ribosomal subunits from Escherichia coli recorded in the electron microscope. The algorithm as used here combines the Single Exposure Conical Reconstruction Technique (SECReT) with a three-dimensional orientation search. The algorithm allows for the refinement of a reconstruction obtained with SECReT by refinement of the true projection angles, and by the inclusion of projections with a priori unknown random orientation. With model data it is demonstrated that the algorithm works reliably even for signal-to-noise ratios lower than 1.