Uncertainty quantification for inverse problems in imaging has drawn much attention lately. Existing approaches towards this task define uncertainty regions based on probable values per pixel, while ignoring spatial correlations within the image, resulting in an exaggerated volume of uncertainty. In this paper, we propose PUQ (Principal Uncertainty Quantification) -- a novel definition and corresponding analysis of uncertainty regions that takes into account spatial relationships within the image, thus providing reduced volume regions. Using recent advancements in stochastic generative models, we derive uncertainty intervals around principal components of the empirical posterior distribution, forming an ambiguity region that guarantees the inclusion of true unseen values with a user confidence probability. To improve computational efficiency and interpretability, we also guarantee the recovery of true unseen values using only a few principal directions, resulting in ultimately more informative uncertainty regions. Our approach is verified through experiments on image colorization, super-resolution, and inpainting; its effectiveness is shown through comparison to baseline methods, demonstrating significantly tighter uncertainty regions.

翻译：图像反问题的不确定性量化近年来备受关注。现有方法基于像素可能值定义不确定性区域，但忽略了图像内部的空域相关性，导致不确定性区域体积被夸大。本文提出PUQ（主成分不确定性量化）——一种考虑图像空间关系的新型不确定性区域定义及其对应分析方法，从而提供体积更小的区域。借助随机生成模型的最新进展，我们围绕经验后验分布的主成分推导不确定性区间，形成能够以用户置信概率保证包含真实未知值的模糊区域。为提升计算效率与可解释性，我们进一步证明仅使用少数主方向即可恢复真实未知值，从而获得更具信息量的不确定性区域。通过图像着色、超分辨率及修复实验验证了该方法有效性，与基线方法对比表明其能显著缩小不确定性区域。