An E cient Fourier Method for 3 D RadonInversion in Exact Cone - Beam

| The 3D Radon transform of an object is an important intermediate result in many analytically exact cone-beam reconstruction algorithms. In this paper, we present a new, highly eecient method for 3D Radon inversion, i.e. reconstruction of the image from the 3D Radon transform, called Direct Fourier Inversion (DFI). The method is based directly on the 3D Fourier Slice Theorem. From the 3D Radon data, which is assumed to be sampled on a polar grid, the 3D object spectrum is calculated by performing FFTs along radial lines in the Radon space. Then, an interpolation is performed from the polar to a cartesian grid using a 3D Gridding step in the frequency domain. Finally, this spectrum is transformed back to the spatial domain via 3D inverse FFT. The algorithm is extremely eecient with computational complexity in the order of N 3 log 2 (N). We have done reconstructions of simulated 3D Radon data assuming sampling conditions and image quality requirements similar to those in medical CT.