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X-ray tomographic reconstruction typically uses voxel basis functions torepresent volumetric images. Due to the structure in voxel basisrepresentations, efficient ray-tracing methods exist allowing fast, GPUaccelerated implementations. Tetrahedral mesh basis functions are a valuablealternative to voxel based image representations as they provide flexible,inhomogeneous partitionings which can be used to provide reconstructions withreduced numbers of elements or with arbitrarily fine object surfacerepresentations. We thus present a robust parallelizable ray-tracing method forvolumetric tetrahedral domains developed specifically for Computed Tomographyimage reconstruction. Tomographic image reconstruction requires algorithms thatare robust to numerical errors in floating point arithmetic whilst typical datasizes encountered in tomography require the algorithm to be parallelisable inGPUs which leads to additional constraints on algorithm choices. Based on theseconsiderations, this article presents numerical solutions to the design ofefficient ray-tracing algorithms for the projection and backprojectionoperations. Initial reconstruction results using CAD data to define atriangulation of the domain demonstrate the advantages of our method andcontrast tetrahedral mesh based reconstructions to voxel based methods.

Numerically robust tetrahedron-based tomographic forward and backward projectors on parallel architectures