BICAV: A block-iterative parallel algorithm for sparse systems with pixel-related weighting

Component averaging (CAV) was recently introduced by Censor, Gordon, and Go rdon as a new iterative parallel technique suitable for large and sparse un structured systems of linear equations. Based on earlier work of Byrne and Censor, it uses diagonal weighting matrices, with pixel-related weights det ermined by the sparsity of the system matrix. CAV is inherently parallel (s imilar to the very slowly converging Cimmino method) but its practical conv ergence on problems of image reconstruction from projections is similar to that of the algebraic reconstruction technique (ART). Parallel techniques a re becoming more important for practical image reconstruction since they ar e relevant not only for supercomputers but also for the increasingly preval ent multiprocessor workstations. This paper reports on experimental results with a block-iterative version of component averaging (BICAV). When BICAV is optimized for block size and relaxation parameters, its very first itera tes are far superior to those of CAV, and more or less on a par with ART. S imilar to CAV, BICAV is also inherently parallel. The fast convergence is d emonstrated on problems of image reconstruction from projections, using the SNARK93 image reconstruction software package. Detailed plots of various m easures of convergence, and reconstructed images are presented.