CT Reconstruction From Parallel and Fan-Beam Projections by a 2-D Discrete Radon Transform

The discrete Radon transform (DRT) was defined by Abervuch et al. as an analog of the continuous Radon transform for discrete data. Both the DRT and its inverse are computable in O(n²logn) operations for images of size n ×n. In this paper, we demonstrate the applicability of the inverse DRT for the reconstruction of a 2-D object from its continuous projections. The DRT and its inverse are shown to model accurately the continuum as the number of samples increases. Numerical results for the reconstruction from parallel projections are presented. We also show that the inverse DRT can be used for reconstruction from fan-beam projections with equispaced detectors.