Enhancing Positron Emission Tomography Image Reconstruction: A Bayesian Approach Incorporating Total Variation and Median Root Prior

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 process of the algorithm comprises two stages. Initially, the MRP algorithm is employed for image reconstruction. Subsequently, the total variation model is applied to attenuate noise within the reconstructed image. Simulation outcomes reveal that the proposed algorithm effectively mitigates Poisson noise while preserving critical image details, such as edges. When contrasted with traditional reconstruction algorithms, the proposed approach enhances both the precision and reliability of PET imaging markedly. Thus, the algorithm carries significant potential for clinical application and could substantially improve the quality of PET imaging.