Equations’ Derivations In The Three-Dimensional Super-Voxel Calculations

Model-Based Iterative Reconstruction (MBIR) is a widely-explored fully 3D Computed Tomography (CT) image reconstruction technique that has a large impact on the image re- construction community. The slow computation speed for MBIR, however, is a bottleneck for scientific advancements in fields that use imaging, such as materials. A recently proposed algorithm, Non-Uniform Parallel Super-Voxel (NU-PSV), utilizes the concept of Three-Dimensional Super-Voxel (3DSV) and Block-Transposed Buffer (BTB) [1]. Experiments in the past show that the NU- PSV algorithm significantly improves the computation speed for MBIR by regularizing data access pattern, reducing cache misses, enabling more parallelism and speeding up algorithmic convergence. This technical report serves as an auxiliary appendix to publication [1]. In this technical report, we demonstrate the theoretical calculations related to a BTB