CT image reconstruction from fan-parallel data

Third generation fan-beam computerized tomography (CT) scanners acquire data one entire projection at a time. The associated filtered-backprojection algorithm requires a computationally expensive pixel-dependent weight factor in the backprojector. Methods of simplifying the reconstruction include rebinning the fan-beam data to parallel projections. The rebinning can be separated into two steps: azimuthal interpolation, leading to the fan-parallel geometry, where data are unevenly spaced on radial lines through the origin of Radon space, and a subsequent axial interpolation to parallel data. Under appropriate view and projection sampling conditions, the azimuthal interpolation can be replaced by either data resorting or projection channel-dependent delays. This article investigates an arcsin algorithm to reconstruct an image directly from the fan-parallel data. Although it is shown that the algorithm cannot be exact, a natural approximation is described. The pre- and postconvolution weights, and the reconstruction filter, are derived analytically. Imaging results demonstrate that arcsin image quality matches that of parallel reconstruction. The fan-parallel reconstruction method eliminates the resolution-compromising axial interpolation and the costly pixel-dependent backprojection weight. Further, an arcsin detector design is proposed for direct parallel reconstruction from fan-beam data.