Fast System Matrix Calculation in CT Iterative Reconstruction

Introduction: Iterative reconstruction techniques provide better image quality and have the potential for reconstructions with lower imaging dose than classical methods in computed tomography (CT). However, the computational speed is major concern for these iterative techniques. The system matrix calculation during the forward- and back projection is one of the most time- consuming components. In this study we propose a method for fast system matrix calculation based on line integral model (LIM) in a simultaneously algebraic reconstruction technique (SART) framework. This method has generality to extend to finite size beam and 3D geometry. Also we use our LIM based method to approximate the area integral for area integral model (AIM) based method. Materials and Methods: First, we calculate the contributing detectors for a given pixel and a given projection view. Then, the lengths of the intersection line from these detectors with the pixel are calculated using an efficient method. To approximate area integral, a narrow fan beam is modeled by several lines that connect the source to one detector cell. Finally the computed system matrix was evaluated by reconstructing the image of a numerical Shepp-Logan phantom, using SART. Results: Overall, numerical results show that our LIM-based method is faster than the Siddon algorithm. Our AIM-based method results in better image quality than LIM-based method but more time consuming. Conclusion: The authors have proposed fast algorithm to calculate system matrix, which are extendable for the finite-size beam and 3D geometry. The algorithm has the potential for parallel computing.