Correspondence analysis of sinogram lines. Sinogram trajectories in factor space replace raw images in the orientation of projections of macromolecular assemblies

The lines of a large group of sinograms of projections with random orientation can be submitted to correspondence analysis. Since the number of samples per line is small, a small matrix is accumulated which is quick to orthogonalise. In the eigenvector space, the lines of a sinogram are represented by points describing a closed trajectory. Two trajectories of different sinograms intersect in the position of their common line. Determining where two trajectories cross each other is a problem of minimum χ2 distance in the space of 5–7 eigenvectors. An algorithm to determine common lines has been implemented and tested with phantom projections oriented at random, and corrupted with noise. The images were simulating a set collected with the two exposures technique, already proposed by the authors for three dimensional reconstruction from random projections. The preliminary models obtained with the new algorithm have been refined by a projection matching based on trajectories. This step requires determining which trajectory, in a set representing computed projections, matches at best with that of an experimental projection. This is a problem of minimum distance in a space with low dimensionality. The present algorithms, based on χ2 distances, run much faster than those based on correlation analysis and the quality of the reconstructed phantoms looks satisfactory.