The combination of positron emission tomography (PET) with magnetic resonance imaging (MRI) may enable novel research in the field of dementia. MR data is commonly used in the analysis of PET data for dementia due to its anatomical information and good soft tissue contrast. PET image reconstruction is currently performed independently of MRI data and the images typically suffer from low resolution, poor signal-to-noise ratio and count dependent bias, due to random error in acquired data and the reconstruction process which is ill-conditioned. The aim of this project is to investigate the benefit of using anatomical information from MR data within PET image reconstruction, applied to dementia research. In this thesis, real PET and MRI patient data of: an amyloid negative healthy elderly volunteer; an amyloid positive elderly patient; and 5 FDG scans of healthy elderly volunteers, were used in order to create realistic ground truth images of the distribution of matter and activity for these individuals. These ground truth images underwent a Monte-Carlo simulation using SimSET, in order to generate simulated raw data of the high resolution research tomograph (HRRT) PET scanner. The simulations were validated by comparing the reconstructed images to real HRRT data, focusing on image resolution. A comparison of partial volume correction (PVC) of PET data applied within image reconstruction with the conventional approach of applying it post-reconstruction was conducted with typical and reduced count levels in order to evaluate the hypothesis that there would be benefit of applying PVC within image reconstruction and that this would have greatest benefit for low count data. Dose reduction by resampling the amyloid negative listmode data was achieved and the same methodology was followed to investigate the benefit of PVC. Finally, raw data from the new GE SIGNA PET-MR scanner of an amyloid positive patient were extracted and reconstructed offline, implementing the same pipeline for PVC. Results showed a little improvement in the recovered activity values is seen when using Lucy-Richardson deconvolution both post and within the image reconstruction. Similarly the use of RM modelling showed little benefit. Differences were observed when using Rousset PVC, with larger differences observed when interleaved with reconstruction. The use of Rousset PVC within reconstruction resulted in a decrease in the bias (average error) for large cortical regions, but an increase in bias was observed for small regions. In general, there were apparent region specific and patient specific variations in the observed bias. For the reduced dose analysis, a similar distribution of the average error was observed as with the full dose results, except from the Lucy-Richardson deconvolution as a post reconstruction method where the bias was significantly increased. Offline reconstruction of the GE SIGNA PET-MR data showed similarities on the distribution of the average error with the amyloid positive results from the HRRT. However due to the lack of a ground truth, the calculation of the bias was not possible. Further work is needed to evaluate the benefit of applying PVC methods for high resolution scanners.