Probabilistic Residual Learning for Aleatoric Uncertainty in Image Restoration

TL;DR

This paper introduces a novel probabilistic residual learning framework that effectively quantifies aleatoric uncertainty in image restoration tasks, providing both high-quality reconstructions and reliable uncertainty estimates.

Contribution

It proposes a multi-level probabilistic modeling approach that improves uncertainty quantification in deep residual learning for image restoration.

Findings

Achieves state-of-the-art point estimates in image restoration

Provides meaningful uncertainty information alongside reconstructions

Demonstrates efficiency in high-dimensional uncertainty sampling

Abstract

Aleatoric uncertainty is an intrinsic property of ill-posed inverse and imaging problems. Its quantification is vital for assessing the reliability of relevant point estimates. In this paper, we propose an efficient framework for quantifying aleatoric uncertainty for deep residual learning and showcase its significant potential on image restoration. In the framework, we divide the conditional probability modeling for the residual variable into a deterministic homo-dimensional level, a stochastic low-dimensional level and a merging level. The low-dimensionality is especially suitable for sparse correlation between image pixels, enables efficient sampling for high dimensional problems and acts as a regularizer for the distribution. Preliminary numerical experiments show that the proposed method can give not only state-of-the-art point estimates of image restoration but also useful associated uncertainty information.