Zhang Muyang, Aykroyd Robert G, Tsoumpas Charalampos
Department of Statistics, School of Mathematics, University of Leeds, Leeds, United Kingdom.
Department of Nuclear Medicine and Molecular Imaging, University Medical Center Groningen, University of Groningen, Groningen, Netherlands.
Front Nucl Med. 2025 Mar 4;5:1508816. doi: 10.3389/fnume.2025.1508816. eCollection 2025.
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.
医学图像受到噪声和相对低分辨率的影响，这在获取生物体的准确和精确测量方面造成了瓶颈。噪声抑制和分辨率增强是逆问题的两个例子。本研究的目的是开发基于基本统计概念的新颖且稳健的估计方法，这些方法可用于解决图像处理中的几个逆问题，并有可能用于图像重建。在本研究中，我们实现了贝叶斯方法，当数据有限但未知数众多时，这些方法已被证明特别有用。具体而言，我们实现了一种局部自适应马尔可夫链蒙特卡罗算法，并通过改变其参数并将其置于不同的实验设置中来分析其稳健性。作为一个应用领域，我们选择了使用原型伽马相机的放射性核素成像。使用模拟数据的结果在边缘恢复、不确定性和偏差方面，将使用所提出方法的估计与当前的非局部自适应方法进行了比较。局部自适应马尔可夫链蒙特卡罗算法更灵活，它在减少估计不确定性和偏差的同时允许更好的边缘恢复。这为医学成像应用带来了更稳健和可靠的输出，从而改善了解释和量化。我们已经表明，与均匀贝叶斯模型相比，使用局部自适应平滑提高了估计精度。
