Block-based iterative coordinate descent

TL;DR: In this article, a block-based version of ICD (B-ICD) is proposed, which computes an update for a block of n voxels simultaneously while accounting for the correlation among the Voxels.

Abstract: 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 [1]. This algorithm in turn can form the basis of powerful model-based iterative reconstruction frameworks for CT reconstruction [2]. In this paper, we will explore a blockbased 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. 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 [3], [4]. For the B-ICD method, however, we form and solve a linear system corresponding to a block of voxels in which we directly account for the correlation. Using this framework, we can update highly correlated voxels whereas with GCD algorithms it is preferable in terms of the resultant relaxation factors to update voxels with little to no correlation.