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 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-defined 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 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：近年来，成像中逆问题的不确定性量化引起了广泛关注。现有方法基于每个像素的可能值定义不确定性区域，但忽略了图像内部的空间相关性，导致不确定性区域体积被夸大。本文提出PUQ（主不确定性量化）——一种考虑图像内部空间关系的新型不确定性区域定义及相应分析方法，从而提供体积更小的不确定性区域。利用生成模型的最新进展，我们在经验后验分布的主成分周围导出不确定性区间，形成一个模糊区域，该区域以用户定义的置信概率保证包含真实未知值。为提高计算效率和可解释性，我们还保证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、超分辨率修复和图像修复实验验证了所提方法，并与基线方法对比展示了其有效性，表明其能显著缩小不确定性区域。