General formulation for X-ray computed tomography

Over recent years, various exact cone-beam reconstruction algorithms have been proposed. The derivations of these algorithms are quite complicated, and often difficult to see the fundamental connections among these methods and their key steps. In this paper, we present a straightforward perspective based on the Fourier transform, which is a universal principle for parallel and divergent beam computed tomography (CT). The formulas in this paper are not only consistent with the latest findings in the field but also valid under more general conditions.