# Probabilistic Residual Learning for Aleatoric Uncertainty in Image Restoration

arXiv: https://arxiv.org/abs/1908.01010 · HTML: https://mlsanity.com/paper/1908.01010/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Aug 2019.

## Built on by (most cited first, 2 of 2)

- [Conditional Variational Autoencoder for Learned Image Reconstruction](https://mlsanity.com/paper/2110.11681/) (2021)
- [Machine Learning Models for Improved Tracking from Range-Doppler Map Images](https://mlsanity.com/paper/2407.03140/) (2024)

## Abstract (arXiv)

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.