A new anisotropic fourth-order diffusion equation model based on image features for image denoising

Abstract

Image denoising has always been a challenging task. For performing this task, one of the most effective methods is based on variational PDE. Inspired by the LLT model, we first propose a new adaptive LLT model by adding a weighted function, and then we propose a class of fourth-order diffusion equations based on the new functional. Owing to the adaptive function, the new functional is better than the LLT model and other fourth-order models in terms of edge preservation. While generalizing the Euler-Lagrange equation of the new functional, we discuss a new fourth-order diffusion framework for image denoising. Different from those of other fourth-order diffusion models, the new diffusion coefficients depend on the first-order and second-order derivatives, which can preserve edges and smooth images, respectively. Regarding numerical implementations, we first design an explicit scheme for the proposed model. However, fourth-order diffusion equations require strict stability conditions, and the number of iterations needed is considerable. Consequently, we apply the fast explicit diffusion algorithm (FED) to the explicit scheme to reduce the time consumption of the proposed approach. Furthermore, the additive operator splitting (AOS) scheme is applied for the numerical implementation, and it is the most efficient among all of our algorithms. Finally, compared with other models, the new model exhibits superior effectiveness and efficiency.