Multicore Performance of Block Algebraic Iterative Reconstruction Methods

Algebraic iterative methods are routinely used for solving the ill-posed sparse linear systems arising in tomographic image reconstruction. Here we consider the Algebraic Reconstruction Techniques (ART) and the Simultaneous Iterative Reconstruction Techniques (SIRT), both of which rely on semi-convergence. Block versions of these methods, based on a partitioning of the linear system, are able to combine the fast semi-convergence of ART with the better multi-core properties of SIRT. These block methods separate into two classes: those that, in each iteration, access the blocks in a sequential manner, and those that compute a result for each block in parallel and then combine these results before the next iteration. The goal of this work is to demonstrate which block methods are best suited for implementation on modern multi-core computers. To compare the performance of the different block methods we use a fixed relaxation parameter in each method, namely, the one that leads to the fastest semi-convergence. Computational results show that for multi-core computers, the sequential approach is preferable.