Fast GPU-based computation of spatial multigrid multiframe LMEM for PET

Significant efforts were invested during the last decade to accelerate PET list-mode reconstructions, notably with GPU devices. However, the computation time per event is still relatively long, and the list-mode efficiency on the GPU is well below the histogram-mode efficiency. Since list-mode data are not arranged in any regular pattern, costly accesses to the GPU global memory can hardly be optimized and geometrical symmetries cannot be used. To overcome obstacles that limit the acceleration of reconstruction from list-mode on the GPU, a multigrid and multiframe approach of an expectation-maximization algorithm was developed. The reconstruction process is started during data acquisition, and calculations are executed concurrently on the GPU and the CPU, while the system matrix is computed on-the-fly. A new convergence criterion also was introduced, which is computationally more efficient on the GPU. The implementation was tested on a Tesla C2050 GPU device for a Gemini GXL PET system geometry. The results show that the proposed algorithm (multigrid and multiframe list-mode expectation-maximization, MGMF-LMEM) converges to the same solution as the LMEM algorithm more than three times faster. The execution time of the MGMF-LMEM algorithm was 1.1 s per million of events on the Tesla C2050 hardware used, for a reconstructed space of \(188 \times 188\times 57\) voxels of \(2\times 2\times 3.15\,\hbox {mm}^3\). For 17- and 22-mm simulated hot lesions, the MGMF-LMEM algorithm led on the first iteration to contrast recovery coefficients (CRC) of more than 75 % of the maximum CRC while achieving a minimum in the relative mean square error. Therefore, the MGMF-LMEM algorithm can be used as a one-pass method to perform real-time reconstructions for low-count acquisitions, as in list-mode gated studies. The computation time for one iteration and 60 millions of events was approximately 66 s.