# On Tensor-Based PDEs and their Corresponding Variational Formulations with Application to Color Image Denoising

arXiv: https://arxiv.org/abs/2608.22302 · HTML: https://mlsanity.com/paper/2608.22302/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 0 of its 21 references that are in the map.
- First posted on arXiv 23 Aug 2026.

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

- [Mapping-Based Image Diffusion](https://mlsanity.com/paper/2608.29164/) (2026)
- [A Tensor Variational Formulation of Gradient Energy Total Variation](https://mlsanity.com/paper/2608.29172/) (2026)

## Abstract (arXiv)

The case when a partial differential equation (PDE) can be considered as an Euler-Lagrange (E-L) equation of an energy functional, consisting of a data term and a smoothness term is investigated. We show the necessary conditions for a PDE to be the E-L equation for a corresponding functional. This energy functional is applied to a color image denoising problem and it is shown that the method compares favorably to current state-of-the-art color image denoising techniques.