3-DIMENSIONAL RECONSTRUCTION FROM CONE-BEAM DATA IN O(N-3 LOG-N) TIME

We have used direct Fourier techniques to modify and implement the 3D reconstruction method from cone-beam projections proposed by Grangeat. In this way we manage to decrease the computational complexity from O(N-4) to O(N-3 log N). Just as Grangeat's original method is exact in the mathematical sense, so is our method, provided a complete set of projection data is acquired. Also in accordance with Grangeat, our algorithm consists of two distinct phases: phase 1, from cone-beam data to derivatives of Radon data; phase 2, from derivatives of Radon data to reconstructed 3D object. In phase 1 we use the direct Fourier method in reverse to obtain line integrals in the detector plane. In phase 2 the 2D linogram method is employed for reconstruction of vertical and horizontal planes in the Radon space.