Recovering the viewing parameters of random, translated and noisy projections of asymmetric objects

A method is described for the determination of the viewing parameters of randomly acquired projections of asymmetric objects. It extends upon the common lines algorithm by determining the relative orientation of projections from the location of lines of intersection among the Fourier transforms of the projections in three-dimensional Fourier space. A new technique for finding the lines of intersection in the presence of translational displacement, and for subsequently finding the translational displacement, is presented. A new technique for dealing with noise is also presented. The complete algorithm is described and its efficacy is demonstrated using real data. This technique may be applied to the three-dimensional reconstruction of viruses, molecules, and cells from in vivo images. It also has many other applications including the reconstruction of underwater scenes, radioastronomy, geoseismic analysis, and portable radiography for medical diagnosis and industrial inspection