Analysis and Simulation of a Coupled Diffusion based Image Denoising Model

Abstract

In this study, a new coupled Partial Differential Equation (CPDE) based image denoising model incorporating space-time regularization into non-linear diffusion is proposed. This proposed model is fitted with additive Gaussian noise which performs efficient image smoothing along with the preservation of edges and fine structures. For this purpose, we propose a new functional minimization framework to remove the image noise, which results in solving a system of three partial differential equations (PDEs). Our proposed model is dissimilar from the existing CPDE models as it includes two additional evolution equations to handle edge strength function and data fidelity term. These two evolution equations control the smoothing process and force the resultant denoised solution to be close to the initial solution. To the best of our knowledge, the proposed model is the only work, which deciphers the combined effect of both the terms using separate PDEs. Furthermore, we establish the existence and uniqueness of a weak solution of the proposed system using the time discretization method with $H^1$ initial data. Finally, we used a generalized weighted average finite difference scheme to efficiently solve the coupled system and experiment results show the effectiveness of the proposed CPDE model.