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(), can be expressed as the sum of three terms:f()=fMO()+fMI()+f N() wherefMO() corresponds to the Feldkamp reconstruction,fMI() represents the information derivable from the circular scan but not utilized in Feldkamp's algorithm, andfN() 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() using Feldkamp's algorithm, (2) compute fMI() using the formula developed in this paper, and (3) estimatefN() using a priori knowledge such as that suggested in Grangeat's algorithm. This study shows that by including the fMI() term, the new algorithm provides more accurate reconstructions than those of Feldkamp even without thefN() estimation.