Anisotropic Diffusion Equation For Image Denoising

How to efficiently pre-process the noisy image in order to get high information is the study focus of image processing. This paper mainly studies the application of anisotropic diffusion in image denoising, and develops new models based on the second-order and fourth-order denoising model, as described next:(1) In the existing second-order anisotropic diffusion denoising model, for the result of the smoothing effect of diffusion coefficient function is not good, the distinction between the image information is inadequate in the smoothing process. To overcome this drawbacks, a new second-order anisotropic diffusion model is proposed. First, a new diffusion-weighted function is designed, which has better smoothness. Then, the new model poses two charateristic indexs including local entropy and structure tensor to finely describe image information. At last,different diffusion coefficients are designed based on the structure tensor . In the smooth regions , the diffusion coefficient is equal to gradient direction and isophotes' direction.However, in the edge regions, diffusion executed only along the isophotes' direction. Numerical experiments show that the proposed model can identify the information such as details and coners except with edges, remove the noises effectively, and maintains the information of the image well.(2) The Y-K fourth-order anisotropic diffusion denoising model can avoid the blocky effects which widely seen in images processed by second-order diffusion. However, the model also has shortcoming of not good noise removing. Also it is almost invalid to the impulse noise and it tends to leave the processed images with isolated back and white speckles. Thus, a new fourth-order anisotropic diffusion model is developed in this paper, in which the diffusion coefficient is dependent on the Laplacian operator, local entropy and the structure tensor.Numerical experiments show that the proposed model retains the advantages of the second-order and the Y-K fourth-order model, overcomes the shortcomings of the two models,and finally achieves better visual results.