Relative to classical methods in computed tomography, iterative reconstruction techniques enable significantly improved image qualities and/or lowered patient doses. However, the computational speed is a major concern for these iterative techniques. In the present study, we present a method for fast system matrix calculation based on the line integral model (LIM) to speed up the computations without compromising the image quality. In addition, we develop a hybrid line–area integral model (AIM) that highlights the advantages of both LIM and AIMs.
The contributing detectors for a given pixel and a given projection view, and the length of corresponding intersection lines with pixels, are calculated using our proposed algorithm. For the hybrid method, the respective narrow-angle fan beam was modeled by multiple equally spaced lines. The computed system matrix was evaluated in the context of reconstruction using the simultaneous algebraic reconstruction technique (SART) as well as maximum likelihood expectation maximization (MLEM).