# On a cross-diffusion system arising in image denosing

## TL;DR

This paper investigates a generalized cross-diffusion system derived from a nonlinear model for image denoising, establishing existence results for solutions and demonstrating its effectiveness through numerical simulations.

## Contribution

It introduces a new cross-diffusion model for image denoising, proving existence of solutions and comparing its performance with scalar models.

## Key findings

- Existence of weak solutions for the static problem.
- Well-posedness of the quasi-steady state approximation.
- Numerical results show competitive denoising performance.

## Abstract

We study a generalization of a cross-diffusion problem deduced from a nonlinear complex-variable diffusion model for signal and image denoising. We prove the existence of weak solutions of the time-independent problem with fidelity terms under mild conditions on the data problem. Then, we show that this translates on the well-posedness of a quasi-steady state approximation of the evolution problem, and also prove the existence of weak solutions of the latter under more restrictive hypothesis. We finally perform some numerical simulations for image denoising, comparing the performance of the cross-diffusion model and its corresponding scalar Perona-Malik equation.