# A Gray Level Indicator-Based Regularized Telegraph Diffusion Equation Applied to Image Despeckling

## TL;DR

This paper introduces a novel non-linear telegraph diffusion model incorporating gray level indicators for effective image despeckling, combining diffusion and wave equations to better preserve textures and oscillations.

## Contribution

The paper presents a new diffusion model that integrates gray level information and wave effects, improving noise removal while maintaining image details.

## Key findings

- Model outperforms recent methods on gray level images with speckle noise.
- The diffusion coefficient depends on both image gradient and gray level.
- Well-posedness of the model is theoretically proven.

## Abstract

In this work, a gray level indicator based non-linear telegraph diffusion model is presented for multiplicative noise removal problem. Most of the researchers focus only on diffusion equation-based model for multiplicative noise removal problem. The suggested model uses the benefit of the combined effect of diffusion equation as well as the wave equation. Wave nature of the model preserves the high oscillatory and texture pattern in an image. In this model, the diffusion coefficient depends not only on the image gradient but also on the gray level of the image, which controls the diffusion process better than only gradient-based diffusion models. Moreover, we prove the well-posedness of the present model using Schauder fixed point theorem. Furthermore, we show the superiority of the proposed model over a recently developed method on a set of gray level test images which are corrupted by speckle noise.