The EM algorithm for PET image reconstruction has two major drawbacks that have impeded the routine use of the EM algorithm: the long computation time due to slow convergence and a large memory required for the image, projection, and probability matrix. An attempt is made to solve these two problems by parallelizing the EM algorithm on multiprocessor systems. An efficient data and task partitioning scheme, called partition-by-box, based on the message passing model is proposed. The partition-by-box scheme and its modified version have been implemented on a message passing system, Intel iPSC/2, and a shared memory system, BBN Butterfly GP1000. The implementation results show that, for the partition-by-box scheme, a message passing system of complete binary tree interconnection with fixed connectivity of three at each node can have similar performance to that with the hypercube topology, which has a connectivity of log(2) N for N PEs. It is shown that the EM algorithm can be efficiently parallelized using the (modified) partition-by-box scheme with the message passing model.

In this paper, we describe how image reconstruction in Computerized Tomography (CT) can be parallelized on a message-passing multiprocessor. In particular, the results obtained from parallel implementation of 3-D CT image reconstruction for parallel beam geometries on the Intel hypercube, iPSC/2, are presented. A two stage pipelining approach is employed for filtering (convolution) and backprojection. The conventional sequential convolution algorithm is modified such that the symmetry of the filter kernel is fully utilized for parallelization.In the backprojection stage, the 3-D Incremental algorithm, our recently developed backprojection scheme which is shown to be faster than conventional algorithm, is parallelized. The speed-up, defined as (sequential processing time)/(parallel processing time), ranging from 5 to 27, and the efficiency, defined as (speed-up)/(the number of processing elements), ranging from 60% to 92%, have been achieved, depending on the size of image and the number of processing elements employed.