This paper presents a Monte Carlo scatter estimation algorithm for Positron Emission Tomography (PET) where positron-electron annihilations induce photon pairs that fly independently in the medium and eventually get absorbed in the detector grid. The path of the photon pair will be a
defined by the detector hits and scattering points where one of the photons changed its direction. The values measured by detector pairs will then be the total contribution, i.e. the integral of such polyline paths of arbitrary length. This integral is evaluated with Monte Carlo quadrature, using a sampling strategy that is appropriate for the graphics processing unit (GPU) that executes the process. We consider the contribution of photon paths to each pair of detectors as an integral over the Cartesian product set of the volume. This integration domain is sampled globally, i.e. a single polyline will represent all annihilation events occurred in any of its points. Furthermore, line segments containing scattering points will be reused for all detector pairs, which allows us to significantly reduce the number of samples. The scatter estimation is incorporated into a PET reconstruction algorithm where the scattered term is subtracted from the measurements.
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