Due to the inherently limited resolution of Positron Emission Tomography (PET) scanners, quantitative measurements taken from PET images suffer from the partial volume averaging of activity across regions of interest. A correction for this effect in PET activity distributions is therefore essential to distinguish differences due to changes in tracer concentration from those due to changes in the volumes of the active brain tissue. Various consequent image post-processing techniques have been developed to address this problem. These operate using associated high resolution anatomical images such as Magnetic Resonance Imaging (MRI), but as well as being highly susceptible to errors in the requisite registration and segmentation procedures, the methods are reliant on unrealistic simplifying assumptions regarding activity distributions in the brain. This work instead couples the correction of PET data to the reconstruction process itself, presenting a two-step scheme using associated MRI data to achieve this. The first step estimates the prior activity distributions from a segmented and intensity transformed MRI image. This is then used in the second step to constrain the Bayesian PET reconstruction with varying degrees of stringency. The prior, or initial correction process, is applied in the form of an energy term, adapted in accordance to an entropy measure taken on the MRI segmentation; i.e., where there is anatomical variation, we assume there also to be activity variation.