Three-dimensional reconstruction from cone-beam data in O(N3logN) time

Abstract

The authors have used direct Fourier techniques to modify and implement the 3D reconstruction method from cone-beam projections proposed by Grangeat (1987, 1991). In this way the authors manage to decrease the computational complexity from O(N⁴) to O(N³logN). Just as Grangeat's original method is exact in the mathematical sense, so is the authors' method, provided a complete set of projection data is acquired. Also in accordance with Grangeat, the authors' 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 the authors 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.