Acceleration of Monte Carlo SPECT simulation using convolution-based forced detection

Monte Carlo (MC) simulation is an established tool to calculate photon transport through tissue in Emission Computed Tomography (ECT). Since the first appearance of MC a large variety of variance reduction techniques (VRT) have been introduced to speed up these notoriously slow simulations. One example of a very effective and established VRT is known as forced detection (FD). In standard FD the path from the photon´s scatter position to the camera is chosen stochastically from the appropriate probability density function (PDF), modeling the distance-dependent detector response. In order to speed up MC the authors propose a convolution-based FD (CFD) which involves replacing the sampling of the PDF by a convolution with a kernel which depends on the position of the scatter event. The authors validated CFD for parallel-hole Single Photon Emission Computed Tomography (SPECT) using a digital thorax phantom. Comparison of projections estimated with CFD and standard FD shows that both estimates converge to practically identical projections (maximum bias 0.9% of peak projection value), despite the slightly different photon paths used in CFD and standard FD. Projections generated with CFD converge, however, to a noise-free projection up to one or two orders of magnitude faster, which is extremely useful in many applications such as model-based image reconstruction