Abstract
Medical images are hampered by noise and relatively low resolution, which create a bottleneck in obtaining accurate and precise measurements of living organisms. Noise suppression and resolution enhancement are two examples of inverse problems. The aim of this study is to develop novel and robust estimation approaches rooted in fundamental statistical concepts that could be utilized in solving several inverse problems in image processing and potentially in image reconstruction. In this study, we have implemented Bayesian methods that have been identified to be particularly useful when there is only limited data but a large number of unknowns. Specifically, we implemented a locally adaptive Markov chain Monte Carlo algorithm and analyzed its robustness by varying its parameters and exposing it to different experimental setups. As an application area, we selected radionuclide imaging using a prototype gamma camera. The results using simulated data compare estimates using the proposed method over the current non-locally adaptive approach in terms of edge recovery, uncertainty, and bias. The locally adaptive Markov chain Monte Carlo algorithm is more flexible, which allows better edge recovery while reducing estimation uncertainty and bias. This results in more robust and reliable outputs for medical imaging applications, leading to improved interpretation and quantification. We have shown that the use of locally adaptive smoothing improves estimation accuracy compared to the homogeneous Bayesian model.