Efficiently GPU-accelerating long kernel convolutions in 3-D DIRECT TOF PET reconstruction via memory cache optimization

The DIRECT represents a novel approach for 3-D Time-of-Flight (TOF) PET reconstruction. Its novelty stems from the fact that it performs all iterative predictor-corrector operations directly in image space. The projection operations now amount to convolutions in image space, using long TOF (resolution) kernels. While for spatially invariant kernels the computational complexity can be algorithmically overcome by replacing spatial convolution with multiplication in Fourier space, spatially variant kernels cannot use this shortcut. Therefore in this paper, we describe a GPU-accelerated approach for this task. However, the intricate parallel architecture of GPUs poses its own challenges, and careful memory and thread management is the key to obtaining optimal results. As convolution is mainly memory-bound we focus on the former, proposing two types of memory caching schemes that warrant best cache memory re-use by the parallel threads. In contrast to our previous two-stage algorithm, the schemes presented here are both single-stage which is more accurate. (orig.)