Ultra-fast hybrid CPU-GPU multiple scatter simulation for 3-D PET.

Scatter correction is very important in 3-D PET reconstruction due to a large scatter contribution in measurements. Currently, one of the most popular methods is the so-called single scatter simulation (SSS), which considers single Compton scattering contributions from many randomly distributed scatter points. The SSS enables a fast calculation of scattering with a relatively high accuracy; however, the accuracy of SSS is dependent on the accuracy of tail fitting to find a correct scaling factor, which is often difficult in low photon count measurements. To overcome this drawback as well as to improve accuracy of scatter estimation by incorporating multiple scattering contribution, we propose a multiple scatter simulation (MSS) based on a simplified Monte Carlo (MC) simulation that considers photon migration and interactions due to photoelectric absorption and Compton scattering. Unlike the SSS, the MSS calculates a scaling factor by comparing simulated prompt data with the measured data in the whole volume, which enables a more robust estimation of a scaling factor. Even though the proposed MSS is based on MC, a significant acceleration of the computational time is possible by using a virtual detector array with a larger pitch by exploiting that the scatter distribution varies slowly in spatial domain. Furthermore, our MSS implementation is nicely fit to a parallel implementation using graphic processor unit (GPU). In particular, we exploit a hybrid CPU-GPU technique using the open multiprocessing and the compute unified device architecture, which results in 128.3 times faster than using a single CPU. Overall, the computational time of MSS is 9.4 s for a high-resolution research tomograph (HRRT) system. The performance of the proposed MSS is validated through actual experiments using an HRRT.