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((r) over right arrow), can be expressed as the sum of three terms:f((r) over right arrow)=f(M0)((r) over right arrow)+f(M1)+((r) over right arrow)+f(N)((r) over right arrow) where f(M0)((r) over right arrow) corresponds to the Feldkamp reconstruction, f(M1)((r) over right arrow) represents the information derivable from the circular scan but not utilized in Feldkamp's algorithm, and f(N)((r) over right arrow) 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 f(M0) ((r) over right arrow) using Feldkamp's algorithm, (2) compute f(M1)((r) over right arrow) using the formula developed in this paper, and (3) estimate f(N)((r) over right arrow) using a priori knowledge such as that suggested in Grangeat's algorithm. This study shows that by including the f(M1)((r) over right arrow) term, the new algorithm provides more accurate reconstructions than those of Feldkamp even without the f(N)((r) over right arrow) estimation.