Fast forward projection and backward projection algorithm using SIMD

Recent developments in PET scanners such as the HRRT (High Resolution Research Tomograph) developed by Siemens greatly enhanced their resolution as well as sensitivity, but they increased coincidence lines of response more than 4.5 times 10 generated by as many nuclear detectors as 120,000. This formidable amount of data poses a real problem in the image reconstruction and its applications. It also has been the major bottleneck in further developments of the higher resolution PET scanners. To remedy this problem in the image reconstruction, we developed a new algorithm based on the SIMD (Single Instruction Multiple Data) technique incorporated with the symmetry properties of the projection and backprojection processes, especially in the 3D OSEM algorithm. We refer to this technique as the SSP (Symmetry and SIMD based Projection-backprojection) algorithm. As a demonstration, the algorithm was applied to the OSEM (Ordered Subset Expectation Maximization) 3D algorithm with HRRT data and it effectively reduced the total image reconstruction time to 80 folds.