Fast Feldkamp algorithm for cone-beam computer tomography

We propose a new fast Feldkamp algorithm for 3-D cone beam tomography with a circular source trajectory. The algorithm is an extension of our recent fast native 2-D fan-beam reconstruction algorithm. It is based on a recursive hierarchical decomposition of the cone-beam backprojection operation into successively smaller sub-volumes. The algorithm reduces the computational complexity of the reconstruction from O(N⁴) to O(N³ log N). Simulations demonstrate the efficiency of our algorithm, with 7-fold speedup for a 128 × 128 × 128 image. Speedups will be much greater for images of more typical size encountered in medicine.