Principal Uncertainty Quantification with Spatial Correlation for Image Restoration Problems
This work addresses uncertainty quantification for image restoration tasks, offering a more efficient and interpretable approach for practitioners in computer vision and medical imaging.
The paper tackles the problem of exaggerated uncertainty volumes in image restoration by proposing PUQ, a method that incorporates spatial correlations to define uncertainty regions, resulting in significantly tighter uncertainty regions compared to baseline methods.
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.