Positron Emission Tomography (PET) holds substantial promise in biomedical research and clinical diagnostics. Nonetheless, PET imaging's constraints, typified by deficient sampling and considerable noise interference, often result in the production of inferior quality reconstructed images. These shortcomings can potentially undermine the clinical utility of the modality. To address this issue, this study introduces a novel image reconstruction algorithm underpinned by Bayesian theory that incorporates the total variation model and the median root prior (MRP) algorithm. The iterative resolution...