Ultra fast 3-D PET image reconstruction using highly compressed, memory-resident system matrices with optimised SIMD access patterns

Fully 3D PET image reconstruction for large detector systems still remains a challenging computational task due to the tremendous number of Lines-of-Response. The reconstruction software PRESTO (PET REconstruction Software TOolkit) allows to use accurate geometrical weighting schemes for the forward/backward projection, e.g. Volume-of-Intersection, while using all measured LORs separately. PRESTO exploits matrix redundancies to realise a strongly compressed, memory-resident system matrix. In this way, the needed time to calculate matrix weights no longer influences the reconstruction time. Nevertheless, in the first implementation the addressing of matrix weights, projection values and voxel values in disfavoured memory access patterns caused severe computational inefficiencies due to the limited memory bandwidth. In this work, the image data and projection data in memory as well as the order of mathematical operations have been re-organised to provide an optimal merit for the Single Instruction Multiple Data (SIMD) approach. A global speedup factor of 15 for has been achieved while obtaining identical results.