Positron emission tomography (PET) has been gaining reputation in the past decades, being a quantitative measurement method for in vivo functional analysis. It is widely used in clinical research and diagnosis, primarily in oncology. Despite its advantages, it has a relatively low spatial resolution due to various technical and physical factors. Therefore, PET measurements usually result in a rather blurry and noisy image, lacking high-frequency components. Partial volume effect (PVE) corresponds to this low resolution as well as the sampling error of the finite voxel grid. PET/CT scanners provide simultaneous PET and registered anatomical data. Based on the assumption that tissue boundaries appear in both modalities, the idea arises to enhance the PET image -- restoring high-frequency data -- using this extra information.
Several approaches are found in the literature, although there is no general method accepted to date. The majority of these methods require some additional a priori information on the scanner or on the region to be analyzed, do not produce corrected images, or pose impractical assumptions. In this thesis, main families of these methods are examined, with respect to their assumptions and applicability given our case.
Furthermore, after a brief summary of existing methods, we propose a novel way of correcting PVE using registered anatomical images. Our method is based on an anisotropic backward diffusion, which is stabilized by a forward approach. True anisotropy is achieved by biasing the process with CT edges. The two processes are combined with custom functions scaling these opposite forces by local features. After the theoretical foundations, implementation details are discussed. Our algorithm was implemented in OpenCL and C++ to harness the benefits of GPU-s. The algorithm was tested against real measured data. Our method successfully enhances region boundaries and restores high-frequency information lost during reconstruction. It performs quite well even in rather noisy environments, especially given that it requires no further a priori information, only the images provided by the scanner(s).