The fast discrete radon transform - I: Theory

A new inversion scheme for reconstruction of images from projections based upon the slope-intercept form of the discrete Radon transform is presented. A seminal algorithm for the forward and the inverse transforms was proposed by Beylkin in 1987. However, as proposed, the original algorithm demonstrated poor dispersion characteristics for steep slopes and could not invert transforms based upon nonlinear slope variations. By formulating the computation as a discrete computation of the continuous Radon transform formula, we explicitly derive fast new generalized inversion methods that overcome the original shortcomings. The generalized forward (FRT) and inverse algorithm (IFRT) proposed are fast, eliminate interpolation calculations, and convert directly between a raster scan grid and a rectangular/polar grid in one step. Part II of this paper describes the implementation of the algorithm on a massively parallel computer, and a new time-domain formulation.