An extended data function and its generalized backprojection for image reconstruction in helical cone-beam CT.

We have recently proposed a general formula (i.e., equations (9) to (11) in Zou and Pan (2004a Phys. Med. Biol. 49 941-59)) for image reconstruction from helical cone-beam data. On the basis of the formula, we have also developed two reconstruction algorithms, which are referred to as the backprojection filtration (BPF) algorithm (Zou and Pan 2004a) and the filtered backprojection (FBP) algorithm (Zou and Pan 2004b Phys. Med. Biol. 49 2717-31), respectively. The two algorithms have been implemented and evaluated in numerical studies. In this note, however, we point out that the data function previously used for proving the general formula in Zou and Pan (2004a) is incomplete and that, instead, an extended data function and its generalized backprojection, which are described in this note, should be used to complete the proof of the general formula. On the other hand, we also demonstrate in this note that the additional term in the extended data function has no effect on the previously developed BPF and FBP algorithms. The results can also be extended to general, smooth trajectories.