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Recent advances in technology have enabled the combination of positron emission tomography (PET) with magnetic resonance imaging (MRI). These PET-MRI scanners simultaneously acquire functional PET and anatomical or functional MRI data. As function and anatomy are not independent of one another the images to be reconstructed are likely to have shared structures. We aim to exploit this inherent structural similarity by reconstructing from both modalities in a joint reconstruction framework. The structural similarity between two modalities can be modelled in two different ways: edges are more likely to be at similar positions and/or to have similar orientations. We analyse the diffusion process generated by minimizing priors that encapsulate these different models. It turns out that the class of parallel level set priors always corresponds to anisotropic diffusion which is sometimes forward and sometimes …