Forward projection of 3D voxel volumes (“X-ray transform”) is one of the central and computation intensive tasks of all iterative tomographic reconstruction algorithms. It is typically implemented using ray driven algorithms such as the often cited Siddon’s algorithm, traversing a voxel volume along connecting lines between X-ray source and detector.
While the texture units of Graphical Processing Units (GPUs) dedicated to fast read-only random memory accesses have long been employed for tomographic reconstruction, their performance advantage cannot be fully utilized in iterative techniques which inherently require steady read-and-write memory accesses to the to-be-reconstructed volume.
With the objective of accelerating iterative cone beam computed tomography (CBCT) reconstruction methods operating solely on read-and-write GPU main memory (RAM), a branchless 3D generalization of Joseph’s projection algorithm is presented that is both highly efficient on GPU RAM and easy to implement.

The presented raycasting algorithm is benchmarked on a recent consumer grade GPU and compared to a DDA algorithm (equivalent to Siddon’s). It outperforms the latter both with respect to memory access rate (factor 3.5) as well as total run time both on GPU RAM and texture memory (factor 1.2). At about 600 (740) GB/s of memory access rate, it computes over 350 (450) projections of a 5123 voxel volume per second on main memory (texture memory).