Fast Hierarchical Backprojection For 3D Radon Transform

Data representing a three-dimensional (3D) sinogram (array of numbers) is backprojected to reconstruct a 3D volume. The transformation requires N.sup.3 log.sub.2 N operations. An input sinogram is subdivided into a plurality of subsinograms using either an exact or approximate decomposition algorithm. The subsinograms are repeatedly subdivided until they represent volumes as small as one voxel. The smallest subsinograrns are backprojected using the direct approach to form a plurality of subvolumes, and the subvolumes are aggregated to form a final volume. Two subdivision algorithms are used. The first is an exact decomposition algorithm, which is accurate, but slow. The second is an approximate decomposition algorithm which is less accurate, but fast. By using both subdivision algorithms appropriately, high quality backprojections are computed significantly faster than existing techniques.