An efficient sparse matrix based parallel image reconstruction algorithm for PET on SP2

The expectation maximization algorithm is an iterative method frequently mentioned in solving the incomplete data problems since its birth in the 1970s. Despite its capability in data approximation, the method has not been widely used in practice due to the huge amount of data involved in the intensive matrix-vector multiplication. We propose a novel technique in speeding up the computation time by better manipulation of the probability matrix. The key idea is to pre-process the input matrix by extracting the non-zero elements along with their index information. We have tested the new algorithm on an IBM SP2 machine for its performance with various configuration settings. Significant amounts of computation time reductions are found in our study depending on the actual density information of the matrix. The new algorithm has the advantage of having a minimum overhead and no new constraint on the matrix structure. With the significant speedup gained from the reduction in computation, our study demonstrates the promising result for future use of the algorithm.