CT reconstruction from parallel and fan-beam projections by 2D discrete Radon transform

We propose two algorithms for the reconstruction of a 2D object from its continuous projections. The first algorithm operates on parallel projection data, while the second uses the more practical model of fan-beam projections. Both algorithms are based on the discrete Radon transform, which extends the continuous Radon transform to discrete data. The discrete Radon transform and its inverse can be computed in a complexity comparable with the 2D FFT, and are shown to accurately model the continuum as the number of samples increases. Numerical results demonstrate high quality reconstructions for both parallel and fan-beam acquisition geometries.