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.