Reconstruction Scheme for Accelerated Maximum Likelihood Reconstruction: The Patchwork Structure

Convergence of iterative algorithms can be improved by updating groups of voxels sequentially rather than updating the whole image simultaneously. The optimal way is to choose groups of uncoupled voxels, i.e. voxels spread over the reconstruction volume. While this is most efficient for convergence reasons, updating groups of spread voxels is less efficient regarding memory access and computational burden. In this work, an image-block update scheme is presented that updates relatively large groups of voxels simultaneously while keeping a considerable gain in convergence. The sequential image-block update can also be combined with ordered subsets. This image-block or patchwork scheme is applied both to transmission and emission maximum likelihood algorithms.