# Whiteness-based bilevel learning of regularization parameters in imaging

arXiv: https://arxiv.org/abs/2403.07026 · HTML: https://mlsanity.com/paper/2403.07026/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 10 Mar 2024.

## Builds on (most cited first, 5 of 5)

- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Bilevel methods for image reconstruction](https://mlsanity.com/paper/2109.09610/) (2021)
- [Bilevel parameter learning for higher-order total variation regularisation models](https://mlsanity.com/paper/1508.07243/) (2015)
- [Adaptive parameter selection for weighted-TV image reconstruction problems](https://mlsanity.com/paper/1905.11264/) (2019)
- [Automatic Tuning of Denoising Algorithms Parameters Without Ground Truth](https://mlsanity.com/paper/2401.09817/) (2024)

## Built on by (most cited first, 4 of 4)

- [Whiteness-based bilevel estimation of weighted TV parameter maps for image denoising](https://mlsanity.com/paper/2503.07814/) (2025)
- [Deep regularization networks for inverse problems with noisy operators](https://mlsanity.com/paper/2506.07008/) (2025)
- [Self-Tuning Regularization for Image Scanning Microscopy](https://mlsanity.com/paper/2605.31426/) (2026)
- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

We consider an unsupervised bilevel optimization strategy for learning regularization parameters in the context of imaging inverse problems in the presence of additive white Gaussian noise. Compared to supervised and semi-supervised metrics relying either on the prior knowledge of reference data and/or on some (partial) knowledge on the noise statistics, the proposed approach optimizes the whiteness of the residual between the observed data and the observation model with no need of ground-truth data.We validate the approach on standard Total Variation-regularized image deconvolution problems which show that the proposed quality metric provides estimates close to the mean-square error oracle and to discrepancy-based principles.