O(N3 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-3 log(2) N) operations for reconstruction of an N x N x N volume from O(N-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-5) computations under the same circumstances.