Radon Transform Techniques for Alignment and Three-dimensional Reconstruction from Random Projections

Since their inception, three-dimensional reconstruction techniques have been based on the theory of Radon transforms. Only much later were Radon transforms recognized as powerful tools for image processing and pattern recognition. Techniques like the common lines technique for finding the orientation of projections of highly symmetrical particles can easily be translated into a technique that uses Radon transforms. Radon transforms have the advantage of being real valued which simplifies many interpolation steps. Correlation techniques have been developed for alignment of a single noisy projection relative to a three-dimensional model and many ideas originally set forward in previous work by the author have been realized. These include simultaneous rotational-translational alignments, iterative refinements of three-dimensional reconstructions and a Two-step Radon Inversion Procedure (TRIP).