# A Tensor Variational Formulation of Gradient Energy Total Variation

arXiv: https://arxiv.org/abs/2608.29172 · HTML: https://mlsanity.com/paper/2608.29172/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 25 references that are in the map.
- First posted on arXiv 29 Aug 2026.

## Builds on (most cited first, 1 of 1)

- [On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising](https://mlsanity.com/paper/2608.22302/) (2026)

## Abstract (arXiv)

We present a novel variational approach to a tensor-based total variation formulation which is called gradient energy total variation, GETV. We introduce the gradient energy tensor [6] into the GETV and show that the corresponding Euler-Lagrange (E-L) equation is a tensor-based partial differential equation of total variation type. Furthermore, we give a proof which shows that GETV is a convex functional. This approach, in contrast to the commonly used structure tensor, enables a formal derivation of the corresponding E-L equation. Experimental results suggest that GETV compares favourably to other state of the art variational denoising methods such as extended anisotropic diffusion (EAD)[1] and total variation (TV) [18] for gray-scale and colour images.