Optimal data replication: a new approach to optimizing parallel EM algorithms on a mesh-connected multiprocessor for 3D PET image reconstruction

The EM algorithm promises an estimated image with the maximal likelihood for 3D PET image reconstruction. However, due to its long computation time, the EM algorithm has not been widely used in practice. While several parallel implementations of the EM algorithm have been developed to make the EM algorithm feasible, they do not guarantee an optimal parallelization efficiency. In this paper, we propose a new parallel EM algorithm which maximizes the performance by optimizing data replication on a mesh-connected message-passing multiprocessor. To optimize data replication, we have formally derived the optimal allocation of shared data, group sizes, integration and broadcasting of replicated data as well as the scheduling of shared data accesses. The proposed parallel EM algorithm has been implemented on an iPSC/860 with 16 PEs. The experimental and theoretical results, which are consistent with each other, have shown that the proposed parallel EM algorithm could improve performance substantially over those using unoptimized data replication