O(N/sup 3/ log N) backprojection algorithm for the 3-D Radon transform

We present a novel backprojection algorithm for three-dimensional (3-D) Radon transform data that requires O(N/sup 3/ log/sub 2/ N) operations for reconstruction of an N/spl times/N/spl times/N volume from O(N/sup 2/) plane-integral projections. Our algorithm uses a hierarchical decomposition of the 3-D Radon transform to recursively decompose the backprojection operation. Simulations are presented demonstrating reconstruction quality comparable to the standard filtered backprojection, which requires O(N/sup 5/) computations under the same circumstances.