A fast and accurate projection algorithm for 3D cone-beam reconstruction with the Algebraic Reconstruction Technique (ART)

The prime motivation of this work is to devise a projection algorithm that makes the Algebraic Reconstruction Technique (ART) and related methods more efficient for routine clinical use without compromising their accuracy. While we focus mostly on a fast implementation of ART-type methods in the context of 3D cone-beam reconstruction, most of the material presented here is also applicable to speed up 2D slice reconstruction from fan-beam data. In this paper, we utilize the concepts of the splatting algorithm, which is a well known and very efficient voxel-driven projection technique for parallel projection, and devise an extension for perspective cone-beam projection that is considerably more accurate than previously outlined extensions. Since this new voxel-driven splatting algorithm must make great sacrifices with regards to computational speed, we describe a new 3D ray-driven projector that uses similar concepts than the voxel-driven projector but is considerably faster, and, at the same time, also more accurate. We conclude that with the proposed fast projection algorithm the computational cost of cone-beam ART can be reduced significantly with the added benefit of slight gains in accuracy. A further conclusion of our studies is that for parallel-beam reconstruction, on the other hand, a simple voxel-driven splatting algorithm provides for more efficient projection.