Mixture prior distributions and Bayesian models for robust radionuclide image processing

The diagnosis of medical conditions and subsequent treatment often involves radionuclide imaging techniques. To refine localisation accuracy and improve diagnostic confidence, compared with the use of a single scanning technique, a combination of two (or more) techniques can be used but with a higher risk of misalignment. For this to be reliable and accurate, recorded data undergo processing to suppress noise and enhance resolution. A step in image processing techniques for such inverse problems is the inclusion of smoothing. Standard approaches, however, are usually limited to applying identical models globally. In this study, we propose a novel Laplace and Gaussian mixture prior distribution that incorporates different smoothing strategies with the automatic model-based estimation of mixture component weightings creating a locally adaptive model. A fully Bayesian approach is presented using multi-level hierarchical modelling and Markov chain Monte Carlo (MCMC) estimation methods to sample from the posterior distribution and hence perform estimation. The proposed methods are assessed using simulated <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>γ</mml:mi> <mml:msup><mml:mtext>-eye</mml:mtext> <mml:mrow><mml:mtext>TM</mml:mtext></mml:mrow> </mml:msup> </mml:math> camera images and demonstrate greater noise reduction than existing methods but without compromising resolution. As well as image estimates, the MCMC methods also provide posterior variance estimates and hence uncertainty quantification takes into consideration any potential sources of variability. The use of mixture prior models, part Laplace random field and part Gaussian random field, within a Bayesian modelling approach is not limited to medical imaging applications but provides a more general framework for analysing other spatial inverse problems. Locally adaptive prior distributions provide a more realistic model, which leads to robust results and hence more reliable decision-making, especially in nuclear medicine. They can become a standard part of the toolkit of everyone working in image processing applications.