Subsets and overrelaxation in iterative image reconstruction

Abstract

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.

Comparison of pharmacokinetic MRI and [18F] fluorodeoxyglucose PET in the diagnosis of breast cancer: initial experience

“…Both attenuation and emission images were iteratively reconstructed by means of a high-overrelaxation single-projection (HOSP) algorithm with optimized overrelaxation parameters [29,30] on a Sun Workstation (Ultra Sparc-II/2, Sun, Mountain View, Calif.). Using this ultra-fast algorithm, six iteration steps were sufficient to accurately quantify regional activity and attenuation values [31]. The discretization of the image matrix was 128 128 pixels with a size of 3.9 3.9 mm 2 .…”

A penalized-likelihood image reconstruction method for emission tomography, compared to postsmoothed maximum-likelihood with matched spatial resolution

“…In this work, we have used either pure MLEM-iterations, or OSEM-schemes in which the number of subsets gradually decreases to unity (pure MLEM). When a fixed and high number of subsets is used for stronger acceleration, OSEM converges to a limit cycle with inferior noise characteristics [22], so the conclusions of our paper cannot be extrapolated to such OSEM schemes.…”

“…1 Since the penalty penalizes only differences, it is expected that the mean count is preserved so . Inserting this in (21) and using (17) yields (22) Switching the order of summations and rearranging a bit we obtain 23which can be rewritten as…”

Iterative Reconstruction Methods

“…52 An alternative approach to controlling the limit cycle is to increase the subset size with iteration, 48 providing results similar to over-relaxation. 53 The similarity in these algorithms leads to some confusion in their applicability, particularly as some of the theoretical concerns are of little clinical relevance e.g. with noisy data the ML solution is undesirable.…”