# A Fuzzy Edge Detector Driven Telegraph Total Variation Model For Image Despeckling

arXiv: https://arxiv.org/abs/1908.01134 · HTML: https://mlsanity.com/paper/1908.01134/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Aug 2019.

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

- [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)
- [A Coupled Fourth Order Telegraph Diffusion Framework Using Grayscale Indicators for Image Despeckling](https://mlsanity.com/paper/2605.00881/) (2026)

## Abstract (arXiv)

Speckle noise suppression is a challenging and crucial pre-processing stage for higher-level image analysis. In this work, a new attempt has been made using telegraph total variation equation and fuzzy set theory for speckle noise suppression. The intuitionistic fuzzy divergence (IFD) function has been used to distinguish between edges and noise. To the best of the author's knowledge, most of the studies on multiplicative speckle noise removal process focus on only diffusion-based filters, and little attention has been paid to the study of fuzzy set theory. The proposed approach enjoy the benefits of both telegraph total variation equation and fuzzy edge detector, which is not only robust to noise but also preserves image structural details. Moreover, we establish the existence and uniqueness of a weak solution of the regularized version of the proposed model using Schauder fixed point theorem. With the proposed model, despeckling is carried out on natural and Synthetic Aperture Radar (SAR) images. The experimental results of the proposed model are reported, which found better in terms of noise suppression and detail/edge preservation, with respect to the existing approaches.