Fast hierarchical backprojection for helical cone-beam tomography

Existing algorithms for exact helical cone beam (HCB) tomographic reconstruction are computationally infeasible for clinical applications. Their computational cost is dominated by 3-D backprojection, which is generally an O(N⁴) operation. We present a fast hierarchical 3-D backprojection algorithm, generalizing fast 2-D parallel beam and fan beam algorithms, which reduces the overall complexity of this step to O(N³ log N), greatly accelerating the reconstruction.