An inversion scheme for reconstruction of images from projections based on the slope-intercept form of the discrete Radon transform is presented. A seminal algorithm for the forward and the inverse transforms proposed by G. Beylkin (1987) demonstrated poor dispersion characteristics for steep slopes and could not invert transforms based on nonlinear slope variations. By formulating the computation of a discrete computation of the continuous Radon transform formula, the authors explicitly derive fast generalized inversion methods that overcome the original shortcomings. The generalized forward (FRT) and inverse (IFRT) algorithms proposed are fast, eliminate interpolation calculations, and convert directly between a raster scan grid and a rectangular/polar grid in one step.