A new cone beam reconstruction algorithm for the circular orbit

It is discovered by reformulating Grangeat´s algorithm that for the circular orbit, an arbitrary function to be reconstructed, f(r&oarr;), can be expressed as the sum of three terms: f(r&oarr;)=f_M0(r&oarr;)+f_M1(r&oarr;)+f_N (r&oarr;), where f_M0(r&oarr;) corresponds to the Feldkamp reconstruction, f_M1(r&oarr;) represents the remaining part of the measurement space component of f(r&oarr;) that cannot be recovered by Feldkamp´s algorithm, and f_N(r&oarr;) represents the null space component of f(r&oarr;). The discrepancy between this finding and the conventional wisdom is caused by the discontinuity of the redundancy function. Thus, a new cone beam reconstruction algorithm for the circular orbit is proposed as follows: 1) compute f_M0(r&oarr;) using Feldkamp´s algorithm; 2) compute f_M1(r&oarr;) using the formula developed here; and 3) estimate f_N(r&oarr;) as suggested in Grangeat´s algorithm. By including the correction term f_M1(r&oarr;), this new algorithm provides a more accurate reconstruction of the measurement space component of f(r&oarr;) than Feldkamp´s algorithm