On the Development of a Coupled Non-linear Telegraph-Diffusion Model for Image Restoration

TL;DR

This paper introduces a novel coupled non-linear telegraph-diffusion PDE model for image restoration that effectively preserves textures and oscillations, outperforming existing hyperbolic-parabolic and diffusion models, especially in noisy conditions.

Contribution

The paper develops a new TCPDE-based framework for image restoration, proving its well-posedness and demonstrating its superiority over existing models in preserving image details.

Findings

Model preserves oscillatory and texture patterns effectively.

Outperforms existing hyperbolic-parabolic PDE models.

Proven to have a unique global weak solution.

Abstract

In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a couple of non-linear telegraph equation and a parabolic equation. Proposed strategy can be applied to significantly preserve the oscillatory and texture pattern in an image, even in low signal-to-noise ratio. First, we prove that the present model has a unique global weak solution using Banach's fixed point theorem. Then apply our model over a set of gray-level images to illustrate the superiority of the proposed model over the recently developed hyperbolic-parabolic PDE based models as well as coupled diffusion-based model.