In this work, we propose a new telegraph coupled partial differential equation (TCPDE) based model for image restoration. New framework interpolates between a coupled wave equation system and a diffusion 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. First, we prove that the present model has a unique global weak solution using Banach 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.