title: Inversion of the 3D Radon transform for a multidetector, point-focused SPECT brain scanner.
abstract: The Radon transform is presented for unattenuated projection data acquired with a multidetector, point-focused SPECT brain scanner. The three-dimensional (3D) integral transform is shown to be exactly invertible only for the case of an ideal machine whose detectors scan away from the source to infinity in all directions. The two-dimensional (2D) ramp filter reconstruction algorithm previously used for this scanner is a limiting case of the 3D method and is exact only for sources with cylindrical symmetry, (f(x,y,z) = f(x,y) for all z). Projection data from a long cylinder and a 1.5 cm thick disc of equal diameters and activity concentrations were simulated by computer for the same scan pattern used on the machine. The data were reconstructed with both the 2D and 3D analytic methods. The 2D method produced a 20% bowl-shaped dip in the centre of the disc, whereas the central slice of the 3D reconstruction was more than 97% accurate. The effective, noise-equivalent sensitivity when reconstructing the central slice of the disc with the necessary 3D method is 10.1 times lower than the sensitivity obtained for the long cylindrical source when reconstructing with the 2D method.
mesh_terms: D001921:Brain / Q000000981:diagnostic imaging*; D006801:Humans; D009010:Monte Carlo Method; D011886:Radon; D012984:Software; D014055:Tomography, Emission-Computed / Q000295:instrumentation*
chemical_list: D011886:Radon