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In this paper, we introduce a new class of projectors for 3D cone beamtomographic reconstruction. We find analytical formulas for the relationshipbetween the voxel volume projected onto a given detector pixel and itscontribution to the extinction value detected on that pixel. Using thisapproach, we construct a near-exact projector and backprojector that can beused especially for algebraic reconstruction techniques. We have implementedthis cutting voxel projector and a less accurate, speed-optimized version of ittogether with two established projectors, a ray tracing projector based onSiddon's algorithm and a TT footprint projector. We show that the cutting voxelprojector achieves, especially for large cone beam angles, noticeably higheraccuracy than the TT projector. Moreover, our implementation of the relaxedversion of the cutting voxel projector is significantly faster than currentfootprint projector implementations. We further show that Siddon's algorithmwith comparable accuracy would be much slower than the cutting voxel projector.All algorithms are implemented within an open source framework for algebraicreconstruction 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, seehttps://github.com/kulvait/KCT_cbct.

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