Fast Implementations of Algebraic Methods for 3D Reconstruction from Cone-Beam Data

The prime motivation of this work is to devise techniques that make the Algebraic Reconstruction Technique (ART) and related methods more efficient for routine clinical use, while not compromising their accuracy. In particular, we strive to push the overall cost for a ART reconstruction as close as possible to the theoretical cost for a reconstruction obtained with Filtered Backprojection (FBP). While we focus mostly on fast implementations of ART-type methods in the context of 3D cone-beam reconstruction, different parts of the material presented here is also applicable to speed up reconstruction from fan-beam and parallel-beam data. It was shown in previous research that three iterations are sufficient to obtain a high quality reconstruction for low-contrast cone-beam. Based on the observation that ART typically only requires only half the projections of FBP, we conclude that if the overall cost for ART’s projection-backprojection operations could be cut in half, then one could obtain an ART implementation whose cost is close to the theoretical cost of FBP. To achieve this goal, we first survey existing projection algorithms and find that these algorithms either lack accuracy or speed, or are not suitable for cone-beam reconstruction. We hence devise a new and more accurate extension to the splatting algorithm, which is a well-known voxeldriven projection method. We also describe a new 3D ray-driven projector that is considerably faster than the voxel-driven projector, and at the same time more accurate and also perfectly suited for the demands of cone-beam. We then devise caching schemes for both ART and Simultaneous ART (SART). These schemes minimize the number of redundant computations for projection and backprojection and, at the same time, are very memory-concious. We conclude that caching and the proposed fast projection algorithm allows the computational cost of ART to be reduced to a level close to FBP’s computational effort.