In this work, we propose a telegraph coupled partial differential equation (TCPDE) based model for image restoration. The new framework interpolates between a couple of nonlinear telegraph equation and a parabolic equation. This proposed strategy can be applied to significantly preserve the oscillatory and texture pattern in an image, even in low signal-to-noise ratio (SNR). First, we prove that the present model has a unique global weak solution using Banach’s fixed point theorem. Then we apply our model over a set of gray level images to illustrate the image denoising ability of the proposed model. The experimental results of the proposed model are reported, which found better in terms of noise elimination and edge preservation, with respect to the recently developed hyperbolic–parabolic PDE based models as well as coupled diffusion-based model.

在这项工作中，我们提出了一种基于电报耦合偏微分方程（TCPDE）的图像恢复模型。新框架在一对非线性电报方程和一个抛物线方程之间进行插值。即使在低信噪比（SNR）下，该提议的策略也可用于显着保留图像中的振荡和纹理图案。首先，我们证明了使用Banach不动点定理的当前模型具有唯一的全局弱解。然后，我们将我们的模型应用于一组灰度图像，以说明所提出模型的图像降噪能力。据报道，提出的模型的实验结果相对于最近开发的基于双曲-抛物线PDE的模型以及基于耦合扩散的模型，在噪声消除和边缘保留方面发现了更好的结果。