Abstract
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.
Abstract (translated)
图像反转问题的不确定性量化最近吸引了很多关注。 existing approaches to this task define uncertainty regions based on probabilistic values per pixel, while neglecting spatial correlation within the image, resulting in an overexaggerated 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. 利用最新的随机生成模型的进步，我们推导了 empirical posterior distribution 中的主要成分的不确定性区间，形成了一种歧义区域，保证了用户有信心情况下包含真正的未观测值。为了改善计算效率和可解释性，我们还保证使用仅几个主要方向仅几步计算就可以恢复真正的未观测值，最终生成更 informative 的不确定性区域。我们的方法通过图像色彩化、超分辨率和填充实验进行了验证；它的有效性通过与基准方法的比较展示了，证明了更加紧密的不确定性区域。
URL
https://arxiv.org/abs/2305.10124
