  In this paper, we first present an arc based algorithm for fan-beam computed
tomography (CT) reconstruction via applying Katsevich's helical CT formula to
2D fan-beam CT reconstruction. Then, we propose a new weighting function to
deal with the redundant projection data. By extending the weighted arc based
fan-beam algorithm to circle cone-beam geometry, we also obtain a new
FDK-similar algorithm for circle cone-beam CT reconstruction. Experiments show
that our methods can obtain higher PSNR and SSIM compared to the
Parker-weighted conventional fan-beam algorithm and the FDK algorithm for
super-short-scan trajectories.
