Fast GPU-based time-of-flight MAP reconstruction with a factored system matrix

We describe the use of relatively low-cost GPU-based processors to implement iterative MAP (Maximum a Posteriori) PET image reconstruction. The algorithm combines accurate system modeling using a factored matrix approach with a preconditioned conjugate gradient method. We describe the procedures used to parallelize the algorithm including use of data reordering schemes and partitioning of calculations to avoid race conditions. Current speed up compared to a quad core CPU is 6.9 using 1 GPU and 10.9 using 2 GPUs. Comparisons of reconstructed images revealed essentially identical images reconstructed using GPU and CPU-only computation. Preliminary results with geometric projection only for GPU-based TOF MAP reconstruction are also presented. Reconstruction using 11 TOF bins takes approximately twice the time per iteration of non-TOF data with the same geometry but also exhibits substantially faster convergence.