**Laszlo Szirmay-Kalos, Balazs Toth, Milan Magdics, David Legrady, and Anton Penzov
Department of Control Engineering and Information Technology, Technical University of Budapest,
Budapest, Magyar tudósok krt. 2, H-1117, HUNGARY
szirmay@iit.bme.hu
**

**Abstract:**

This paper proposes a Monte Carlo algorithm for gamma-photon transport, that partially reuses random paths and is appropriate for parallel GPU implementation. According to the requirements of the application of the simulation results in reconstruction algorithms, the method aims at similar relative rather than absolute errors of the detectors. The resulting algorithm is SIMD-like, which is a requirement of efficient GPU implementation, i.e. all random paths are built with the same sequence of instructions, thus can be simulated on parallel threads that practically have no conditional branches. The algorithm is a combined method that separates the low-dimensional part that cannot be well mimicked by importance sampling and computes it by a deterministic quadrature, while the high-dimensional part that is made low-variation by importance sampling is handled by the Monte Carlo method. The deterministic quadrature is based on a geometric interpretation of a direct, i.e. non-scattered effect of a photon on all detectors.

**Keywords:**

Importance sampling, Klein-Nishina phase function, Compton scattering, CUDA