Block-based iterative coordinate descent

In the context of X-ray computed tomography (CT), the iterative coordinate descent (ICD) algorithm is a reconstruction algorithm that computes image updates on a voxel-by-voxel basis. This algorithm in turn can form the basis of powerful model-based iterative reconstruction frameworks for CT reconstruction . In this paper, a block based version of ICD (B-ICD) that computes an update for a block of N voxels simultaneously while accounting for the correlation among the N voxels is explored. Previous studies investigating grouped updates in a coordinate descent (GCD) framework include updating a group of potentially correlated or coupled voxels using an under-relaxation factor that preserves convergence . For the B-ICD method, however, this paper forms and solves a linear system corresponding to a block of voxels in which the correlation is directly accounted for. Using this framework, highly correlated voxels is updated whereas with GCD algorithms it is preferable in terms of the resultant relaxation factors to update voxels with little to no correlation.