Principal Uncertainty Quantification With Spatial Correlation for Image Restoration Problems

Area of Science:

• Computational imaging
• Statistical modeling
• Machine learning

Background:

• Uncertainty quantification (UQ) in inverse imaging problems is crucial.
• Current UQ methods often ignore spatial correlations, leading to overestimated uncertainty volumes.
• There is a need for UQ methods that provide accurate and spatially aware uncertainty estimates.

Purpose of the Study:

• To introduce Principal Uncertainty Quantification (PUQ), a novel approach for UQ in imaging.
• To develop a method that accounts for spatial correlations within images for reduced uncertainty regions.
• To ensure guaranteed inclusion of true unseen values within user-defined confidence probabilities.

Main Methods:

• Leveraging advancements in generative models to define uncertainty intervals.
• Deriving intervals around principal components of the empirical posterior distribution.
• Utilizing a reduced set of principal directions for computational efficiency and interpretability.

Main Results:

• PUQ generates significantly tighter uncertainty regions compared to baseline methods.
• The approach effectively accounts for spatial relationships within images.
• Experiments in image colorization, super-resolution, and inpainting demonstrate PUQ's effectiveness.

Conclusions:

• PUQ offers a more accurate and efficient approach to uncertainty quantification in imaging.
• The method provides more informative and reduced uncertainty regions by incorporating spatial correlations.
• PUQ represents a significant advancement in UQ for inverse problems in image analysis.