Abstract
Since Katsevich's work on cone-beam CT in 2002, a series of new reconstruction formulae for cone-beam and fan-beam reconstruction have been published. To understand these new results in a unified way, two schemes were proposed in the literature: one is based on the Radon formula, while the other on the Tuy formula. In the paper, we present a general two-step scheme for parallel-, fan- and cone-beam CT based on the inverse Fourier transform. We first derive parallel-beam formulae and then translate them to the divergent-beam case via a standardized method. This complete framework not only provides a single mechanism for the deduction of most existing CT formulae but also generates new algorithms. Meanwhile, along the development of this new framework some minor flaws are identified and fixed in publications. Additionally, the traditional assumption that an object be compactly supported inside a scanning trajectory is no longer needed.