Accelerating the anti-aliased algebraic reconstruction technique (ART) by table-based voxel backward projection

ART is often used in CT for 2D or 3D reconstruction when the projections are sparse, noisy, or non-uniformly distributed. Recently, ART was also shown to be useful for PET. Reconstructions obtained with ART often exhibit considerable noise artifacts attributable to aliasing introduced in both grid projection and reprojection. While the table-assisted raycasting approach currently used for projection and reprojection allows some of the necessary anti-aliasing measures to be implemented efficiently, certain limitations remain: 1) Anti-aliasing by projection supersampling is time consuming; 2) An implementation on parallel architectures is awkward. Here, the authors show how the ART projection process can be reversed into a backward-viewing block-iterative procedure. The reconstruction grid voxels are projected independently to the screen where their contributions accumulate. In this way, the overhead associated with stepping individual rays across the grid is eliminated. The "footprint" of a voxel's contribution is realized as a pre-computed lookup-table, and most projection operations are reduced to simple incremental operations and table lookups. The authors' approach cuts the cost for ART with respect to equivalent raycasting methods by about 30% while using much less memory. Finally, the independency of calculations among voxels facilitates a parallel implementation.