# Bilevel parameter learning for higher-order total variation regularisation models

arXiv: https://arxiv.org/abs/1508.07243 · HTML: https://mlsanity.com/paper/1508.07243/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Aug 2015.

## Built on by (most cited first, 14 of 14)

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- [Oracle Supervision Transfers for Hyperparameter Prediction in Model-Based Image Denoising](https://mlsanity.com/paper/2605.20479/) (2026)

## Abstract (arXiv)

We consider a bilevel optimisation approach for parameter learning in higher-order total variation image reconstruction models. Apart from the least squares cost functional, naturally used in bilevel learning, we propose and analyse an alternative cost, based on a Huber regularised TV-seminorm. Differentiability properties of the solution operator are verified and a first-order optimality system is derived. Based on the adjoint information, a quasi-Newton algorithm is proposed for the numerical solution of the bilevel problems. Numerical experiments are carried out to show the suitability of our approach and the improved performance of the new cost functional. Thanks to the bilevel optimisation framework, also a detailed comparison between TGV2 and ICTV is carried out, showing the advantages and shortcomings of both regularisers, depending on the structure of the processed images and their noise level.