Statistical iterative methods are a widely used method of image reconstruction in emission tomography. Traditionally, the image\r\nspace is modelled as a combination of cubic voxels as a matter of simplicity. After reconstruction, images are routinely filtered to\r\nreduce statistical noise at the cost of spatial resolution degradation. An alternative to produce lower noise during reconstruction\r\nis to model the image space with spherical basis functions. These basis functions overlap in space producing a significantly large\r\nnumber of non-zero elements in the system response matrix (SRM) to store, which additionally leads to long reconstruction times.\r\nThese two problems are partly overcome by exploiting spherical symmetries, although computation time is still slower compared\r\nto non-overlapping basis functions. In this work, we have implemented the reconstruction algorithm using Graphical Processing\r\nUnit (GPU) technology for speed and a precomputedMonte-Carlo-calculated SRM for accuracy. The reconstruction time achieved\r\nusing spherical basis functions on a GPU was 4.3 times faster than the Central Processing Unit (CPU) and 2.5 times faster than\r\na CPU-multi-core parallel implementation using eight cores. Overwriting hazards are minimized by combining a random line of\r\nresponse ordering and constrained atomic writing. Small differences in image quality were observed between implementations.
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