An improved cone‐beam reconstruction algorithm for the circular orbit

By reformulating Grangeat's algorithm for the circular orbit, it is discovered that an arbitrary function to be reconstructed, f({article}{empty}{document}r^ →{document} ), can be expressed as the sum of three terms:f({article}{empty}{document}r^ →{document} )=fMO({article}{empty}{document}r^ →{document} )+fMI({article}{empty}{document}r^ →{document} )+f N({article}{empty}{document}r^ →{document} ) wherefMO({article}{empty}{document}r^ →{document} ) corresponds to the Feldkamp reconstruction,fMI({article}{empty}{document}r^ →{document} ) represents the information derivable from the circular scan but not utilized in Feldkamp's algorithm, andfN({article}{empty}{document}r^ →{document} ) represents the information which cannot be derived from the circular scanning geometry. Thus, a new cone‐beam reconstruction algorithm for the circular orbit is proposed as follows: (1) compute fMO({article}{empty}{document}r^ →{document} ) using Feldkamp's algorithm, (2) compute fMI({article}{empty}{document}r^ →{document} ) using the formula developed in this paper, and (3) estimatefN({article}{empty}{document}r^ →{document} ) using a priori knowledge such as that suggested in Grangeat's algorithm. This study shows that by including the fMI({article}{empty}{document}r^ →{document} ) term, the new algorithm provides more accurate reconstructions than those of Feldkamp even without thefN({article}{empty}{document}r^ →{document} ) estimation.