Parallelizable algorithms for X-ray CT image reconstruction with spatially non-uniform updates

Statistical image reconstruction methods for X-ray CT provide good images even for reduced dose levels but require substantial compute time. Iterative algorithms that converge in fewer iterations are preferable. Spatially non-homogeneous iterative coordinate descent (NH-ICD) accelerates convergence by updating more frequently the voxels that are predicted to change the most between the current image and the final image. However, the sequential update of NH-ICD reduces parallelism opportunities. This paper focuses on iterative algorithms that are more amenable to parallelization, namely the axial block coordinate descent (ABCD) algorithm and an ordered subsets algorithm based on separable quadratic surrogates (OS-SQS), because these have the potential to be faster than ICD in multiprocessor implementations. We first adapt the “non-homogeneous” approach to ABCD, which simply requires updating more frequently the axial blocks that are predicted to change the most during convergence. More interestingly, we derive a new version of the OS-SQS algorithm that leads to spatially non-uniform updates with larger step sizes for the voxels that are predicted to change the most between the current image and the final image. The single subset version of this algorithm is still guaranteed to converge monotonically. We use a 3D patient CT scan to demonstrate that the proposed algorithms with spatially non-uniform updates converge faster than the ordinary algorithms. In particular, the NU approach accelerated the OS-SQS algorithm by a factor of three.