# Well-posedness study of a non-linear hyperbolic-parabolic coupled system applied to image speckle reduction

## TL;DR

This paper analyzes a non-linear hyperbolic-parabolic coupled system for image despeckling, establishing its well-posedness and demonstrating its effectiveness through numerical experiments on noisy images.

## Contribution

It introduces a new coupled system based on telegraph diffusion for despeckling and proves its well-posedness using Schauder's fixed point theorem.

## Key findings

- The model effectively reduces speckle noise in images.
- Numerical results outperform recent models.
- The system's well-posedness is rigorously established.

## Abstract

In this article, we consider a non-linear hyperbolic-parabolic coupled system based on telegraph diffusion framework applied to image despeckling. A separate equation is used to calculate the edge variable, which improves the quality of the despeckled images. A well-posedness result of the proposed coupled system is settled via Schauder's fixed point theorem. Numerical experiments are reported to illustrate the effectiveness of the proposed model, with recently developed models, over a set of gray level test images contaminated by speckle noise.