  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.
