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. 2024 Sep 5;4:1380518. doi: 10.3389/fnume.2024.1380518. eCollection 2024.
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 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.
医疗状况的诊断及后续治疗通常涉及放射性核素成像技术。为提高定位精度并增强诊断可信度，与使用单一扫描技术相比，可采用两种（或更多）技术的组合，但存在更高的对准错误风险。为确保其可靠且准确，记录的数据需进行处理以抑制噪声并提高分辨率。图像处理技术中针对此类逆问题的一个步骤是进行平滑处理。然而，标准方法通常局限于全局应用相同的模型。在本研究中，我们提出一种新颖的拉普拉斯和高斯混合先验分布，该分布结合了不同的平滑策略，并基于自动模型估计混合成分权重，从而创建一个局部自适应模型。我们提出了一种全贝叶斯方法，使用多级分层建模和马尔可夫链蒙特卡罗（MCMC）估计方法从后验分布中采样，进而进行估计。使用模拟相机图像对所提出的方法进行评估，结果表明其比现有方法具有更强的降噪能力，且不影响分辨率。除了图像估计外，MCMC方法还提供后验方差估计，因此不确定性量化考虑了任何潜在的变异性来源。在贝叶斯建模方法中使用混合先验模型（部分为拉普拉斯随机场，部分为高斯随机场）并不局限于医学成像应用，而是为分析其他空间逆问题提供了一个更通用的框架。局部自适应先验分布提供了一个更现实的模型，可得出稳健的结果，从而实现更可靠的决策，尤其是在核医学领域。它们可以成为图像处理应用领域所有从业者工具包中的标准组成部分。
