Noise performance of fast hierarchical 3D backprojection for helical cone-beam tomography

Existing algorithms for exact helical cone beam tomographic reconstruction involve a 3-D backprojection step, which dominates the computational cost of the algorithm. Hierarchical backprojection reduces the complexity of this step from O(N⁴) to O(N³logN), greatly accelerating the reconstruction process. Here the performance of the hierarchical reconstruction is examined in the presence of noise. We demonstrate that reconstructions obtained using this method have good image quality and comparable noise performance to conventional backprojection, while providing a speedup in computation by over an order of magnitude. These properties are essential for acceptance of a fast reconstruction algorithm.