Fully 3D iterative scatter-corrected OSEM for HRRT PET using a GPU

Accurate scatter correction is especially important for high-resolution 3D positron emission tomographies (PETs) such as high-resolution research tomograph (HRRT) due to large scatter fraction in the data. To address this problem, a fully 3D iterative scatter-corrected ordered subset expectation maximization (OSEM) in which a 3D single scatter simulation (SSS) is alternatively performed with a 3D OSEM reconstruction was recently proposed. However, due to the computational complexity of both SSS and OSEM algorithms for a high-resolution 3D PET, it has not been widely used in practice. The main objective of this paper is, therefore, to accelerate the fully 3D iterative scatter-corrected OSEM using a graphics processing unit (GPU) and verify its performance for an HRRT. We show that to exploit the massive thread structures of the GPU, several algorithmic modifications are necessary. For SSS implementation, a sinogram-driven approach is found to be more appropriate compared to a detector-driven approach, as fast linear interpolation can be performed in the sinogram domain through the use of texture memory. Furthermore, a pixel-driven backprojector and a ray-driven projector can be significantly accelerated by assigning threads to voxels and sinograms, respectively. Using Nvidia's GPU and compute unified device architecture (CUDA), the execution time of a SSS is less than 6 s, a single iteration of OSEM with 16 subsets takes 16 s, and a single iteration of the fully 3D scatter-corrected OSEM composed of a SSS and six iterations of OSEM takes under 105 s for the HRRT geometry, which corresponds to acceleration factors of 125x and 141x for OSEM and SSS, respectively. The fully 3D iterative scatter-corrected OSEM algorithm is validated in simulations using Geant4 application for tomographic emission and in actual experiments using an HRRT.