Subsets and overrelaxation in iterative image reconstruction

A number of iterative image reconstruction algorithms were integrated into one formula characterizing each algorithm by only two parameters: overrelaxation and number of subsets. From the formula it follows that the ordered-subsets iteration (OS-EM) is equivalent to iteration with overrelaxation, where the OS level corresponds to the overrelaxation parameter. Algorithms represented by the formula were studied with respect to speed of convergence and image characteristics. In particular, OS-EM was compared with a single-projection iteration procedure using an optimized sequence of overrelaxation parameters (HOSP) which combines rapid convergence with reduced storage requirements. As a result, OS-EM with a constant number of subsets either needed more iteration steps than HOSP or provoked additional noise, depending on the number of subsets used during iteration. OS-EM can be improved by using decreasing OS levels, imitating the decreasing overrelaxation parameters used for HOSP. The resulting OS-EM may be slightly more rapid than HOSP, due to the increasing number of projections used simultaneously.