PET (Positron Emission Tomography) is a method for medical imaging, which helps to reconstruct a three-dimensional image of various parts of human body. Before the measurement positron emitting substance is injected into the body, when collision occurs between a positron and electron, they annihilate each other while emitting two gamma photons in opposite directions. Each gamma photon has 511 keV energy. During the measurement a detector ring is set up around the body, which is able to detect the incoming gamma photons with the help of a detector crystal grid on its modules. The eletronic parts of the modules try to match the detected photons in a given time window, and they register a 5D data which contains the index of the module pair and the coordinates of crystals on the modules, where the two hits were registered about the same time. This 5D data is called LOR (Line Of Response). The goal of the measurement is to get the hit count for each LOR in the detector ring, after that the density of gamma photon emission can be computed in a given volume of interest. This data corresponds to the emission density of the injected radioactive substance, which gives valuable information about various diseases in the early stage. The reconstruction is an iterative process, which contains forward and back projection, the forward projection is int he focus of this document. In this case a given emission density is assumed in the volume of interest, and following a physical model, the PET framework tries to reconstruct the trajectory of the gamma photons.
After the photon reaches the surface, it continues to travel and scatter inside the crystal grid before an eletronic detector finally registers the hit. The main topic of this thesis to give a mathematical approach to describe the inter-crystal scattering and to implement filters on GPU efficiently to simulate this effect. However, the computation complexity of the filter evaluation is too high for today’s GPUs. The goal is to construct the best possible estimator that yields a realistic process time for the task when executed on a graphic card.