  We present a new algorithm for 3D cone-beam tomography. The algorithm is
based on decomposition of the cone-beam backprojection operation and angular
decimation. It has computational complexity of $O(N^{3.5})$ and allows
considerable reduction of peak memory usage in comparison with conventional
algorithms. Tests with real data demonstrate the acceleration, achieved by
using our algorithm instead of FDK, with 20-fold speedup for a $2000 \times
2000 \times 720$ image. The algorithm is compared with other fast FDK
algorithms.
