# A study of the one dimensional total generalised variation regularisation problem

arXiv: https://arxiv.org/abs/1309.5900 · HTML: https://mlsanity.com/paper/1309.5900/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Sep 2013.

## Built on by (most cited first, 1 of 1)

- [Learning spatially varying regularisation parameters of low regularity for image reconstruction](https://mlsanity.com/paper/2608.25127/) (2026)

## Abstract (arXiv)

In this paper we study the one dimensional second order total generalised variation regularisation (TGV) problem with L2 data fitting term. We examine some properties of this model and we calculate exact solutions using simple piecewise affine functions as data terms. We investigate how these solutions behave with respect to the TGV parameters and we verify our results using numerical experiments.