# New Fourth-Order Grayscale Indicator-Based Telegraph Diffusion Model for Image Despeckling

arXiv: https://arxiv.org/abs/2509.26010 · HTML: https://mlsanity.com/paper/2509.26010/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 0 of its 29 references that are in the map.
- First posted on arXiv 30 Sep 2025.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Built on by (most cited first, 3 of 3)

- [Comparative Study of Weighted and Coupled Second- and Fourth-Order PDEs for Image Despeckling in Grayscale, Color, SAR, and Ultrasound](https://mlsanity.com/paper/2604.23612/) (2026)
- [Single Image Defogging Using a Fourth-Order Telegraph PDE Guided by Physical Haze Modeling](https://mlsanity.com/paper/2605.00878/) (2026)
- [A Coupled Fourth Order Telegraph Diffusion Framework Using Grayscale Indicators for Image Despeckling](https://mlsanity.com/paper/2605.00881/) (2026)

## Abstract (arXiv)

Second-order PDE models have been widely used for suppressing multiplicative noise, but they often introduce blocky artifacts in the early stages of denoising. To resolve this, we propose a fourth-order nonlinear PDE model that integrates diffusion and wave properties. The diffusion process, guided by both the Laplacian and intensity values, reduces noise better than gradient-based methods, while the wave part keeps fine details and textures. The effectiveness of the proposed model is evaluated against two second-order anisotropic diffusion approaches using the Peak Signal-to-Noise Ratio (PSNR) and Mean Structural Similarity Index (MSSIM) for images with available ground truth. For SAR images, where a noise-free reference is unavailable, the Speckle Index (SI) is used to measure noise reduction. Additionally, we extend the proposed model to study color images by applying the denoising process independently to each channel, preserving both structure and color consistency. The same quantitative metrics PSNR and MSSIM are used for performance evaluation, ensuring a fair comparison across grayscale and color images. In all the cases, our computed results produce better results compared to existing models in this genre.