Bayesian statistics is a cornerstone of imaging sciences, underpinning many and varied approaches from Markov random fields to score-based denoising diffusion models. In addition to powerful image estimation methods, the Bayesian paradigm also provides a framework for uncertainty quantification and for using image data as quantitative evidence. These probabilistic capabilities are important for the rigorous interpretation of experimental results and for robust interfacing of quantitative imaging pipelines with scientific and decision-making processes. However, are the probabilities delivered by existing Bayesian imaging methods meaningful under replication of an experiment, or are they only meaningful as subjective measures of belief? This paper presents a Monte Carlo method to explore this question. We then leverage the proposed Monte Carlo method and run a large experiment requiring 1,000 GPU-hours to probe the accuracy of five canonical Bayesian imaging methods that are representative of some of the main Bayesian imaging strategies from the past decades (a score-based denoising diffusion technique, a plug-and-play Langevin algorithm utilising a Lipschitz-regularised DnCNN denoiser, a Bayesian method with a dictionary-based prior trained subject to a log-concavity constraint, an empirical Bayesian method with a total-variation prior, and a hierarchical Bayesian Gibbs sampler based on a Gaussian Markov random field model). We find that, a few cases, the probabilities reported by modern Bayesian imaging techniques are in broad agreement with long-term averages as observed over a large number of replication of an experiment, but existing Bayesian imaging methods are generally not able to deliver reliable uncertainty quantification results.

翻译：贝叶斯统计是成像科学的基石，支撑着从马尔可夫随机场到基于分数的去噪扩散模型等多种方法。除了强大的图像估计方法外，贝叶斯范式还为不确定性量化以及将图像数据作为定量证据提供了框架。这些概率能力对于严格解释实验结果以及将定量成像流程与科学和决策过程稳健对接至关重要。然而，现有的贝叶斯成像方法输出的概率在实验重复下是否具有实际意义，抑或仅仅作为主观信念度量？本文提出了一种蒙特卡洛方法来探索这一问题。随后，我们利用所提出的蒙特卡洛方法开展了一项需要1000 GPU小时的大规模实验，以检验五种代表性贝叶斯成像方法的准确性，这些方法涵盖了近几十年来主要贝叶斯成像策略（一种基于分数的去噪扩散技术、一种利用Lipschitz正则化DnCNN去噪器的即插即用朗之万算法、一种基于对数凹性约束的字典先验贝叶斯方法、一种采用全变分先验的经验贝叶斯方法，以及一种基于高斯马尔可夫随机场模型的层次贝叶斯吉布斯采样器）。我们发现，在少数情况下，现代贝叶斯成像技术报告的概率与大量实验重复下的长期平均值大致一致，但现有贝叶斯成像方法普遍无法提供可靠的不确定性量化结果。