On the efficiency of iterative ordered subset reconstruction algorithms for acceleration on GPUs

Expectation Maximization (EM) and the Simultaneous Iterative Reconstruction Technique (SIRT) are two iterative computed tomography reconstruction algorithms often used when the data contain a high amount of statistical noise, have been acquired from a limited angular range, or have a limited number of views. A popular mechanism to increase the rate of convergence of these types of algorithms has been to perform the correctional updates within subsets of the projection data. This has given rise to the method of Ordered Subsets EM (OS-EM) and the Simultaneous Algebraic Reconstruction Technique (SART). Commodity graphics hardware (GPUs) has shown great promise to combat the high computational demands incurred by iterative reconstruction algorithms. However, we find that the special architecture and programming model of GPUs add extra constraints on the real-time performance of ordered subsets algorithms, counteracting the speedup benefits of smaller subsets observed on CPUs. This gives rise to new relationships governing the optimal number of subsets as well as relaxation factor settings for obtaining the smallest wall-clock time for reconstruction-a factor that is likely application-dependent. In this paper we study the generalization of SIRT into Ordered Subsets SIRT and show that this allows one to optimize the computational performance of GPU-accelerated iterative algebraic reconstruction methods.