Cutting Voxel Projector a New Approach to Construct 3D Cone Beam CT Operator

In this paper, we introduce a new class of projectors for 3D cone beam tomographic reconstruction. We find analytical formulas for the relationship between the voxel volume projected onto a given detector pixel and its contribution to the extinction value detected on that pixel. Using this approach, we construct a near-exact projector and backprojector that can be used especially for algebraic reconstruction techniques. We have implemented this cutting voxel projector and a less accurate, speed-optimized version of it together with two established projectors, a ray tracing projector based on Siddon's algorithm and a TT footprint projector. We show that the cutting voxel projector achieves, especially for large cone beam angles, noticeably higher accuracy than the TT projector. Moreover, our implementation of the relaxed version of the cutting voxel projector is significantly faster than current footprint projector implementations. We further show that Siddon's algorithm with comparable accuracy would be much slower than the cutting voxel projector. All algorithms are implemented within an open source framework for algebraic reconstruction in OpenCL 1.2 and C++ and are optimized for GPU computation. They are published as open-source software under the GNU GPL 3 license, see https://github.com/kulvait/KCT_cbct.