# Asymptotic behaviour of total generalised variation

arXiv: https://arxiv.org/abs/1502.06933 · HTML: https://mlsanity.com/paper/1502.06933/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2015.

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

- [Deep unrolling for learning optimal spatially varying regularisation parameters for Total Generalised Variation](https://mlsanity.com/paper/2502.16532/) (2025)
- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

The recently introduced second order total generalised variation functional TGVβ,α2 has been a successful regulariser for image processing purposes. Its definition involves two positive parameters α and β whose values determine the amount and the quality of the regularisation. In this paper we report on the behaviour of TGVβ,α2 in the cases where the parameters α, β as well as their ratio β/α becomes very large or very small. Among others, we prove that for sufficiently symmetric two dimensional data and large ratio β/α, TGVβ,α2 regularisation coincides with total variation (TV) regularisation.