Anisotropic second and fourth order diffusion models based on Convolutional Virtual Electric Field for image denoising

This paper proposes novel second order and fourth order anisotropic diffusion models for image denoising. These two models are based on CONvolutional Virtual Electric Field (CONVEF). The proposed second order anisotropic diffusion model was introduced by introducing the CONVEF into the Perona–Malik (P–M) equation and the fourth order one is coined by combining CONVEF and the You–Kaveh (Y–K) equation. The employment of the CONVEF model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise. In addition, the proposed CONVEF-based Y–K model is an anisotropic diffusion equation which can avoid the over-smoothness of edges and provide better edge protection capability except for better denoising. Some experiments are conducted to demonstrate the efficiency of the proposed methods.