Image Denoising Based On Partial Differential Equations And Enhance Research

The image denoising and enhancement is an important branch in the digital image processing area. It includes two parts contents:removing the noise of the images and enhancing the information of image edge. Partial differential equation of the image processing experienced the process of linear diffusion equation, nonlinear diffusion equation and anisotropic nonlinear diffusion equation. In recent years, there are two kinds of processing method, high order diffusion equation and complex diffusion equation, appear in the partial differential equation of image processing area.This paper detailedly researched the partial differential equations of the image denoising. Firstly, we briefly introduced the rudimentary knowledge of partial differential equation of the image processing, then we discussed the typical image denoising partial differential equation model. We selected the most classic P-M Diffusion Model to study. It has very good denoising ability. Because of the nonlinearity, it can, to a certain extent, keep the edge when removing noise. According to the shortcomings of P-M Diffusion Model, this paper puts forward an Improved Model. According to the characteristics of the diffusion coefficients, we improved the diffusion coefficients to better keep image edge. However, because the gradient is the edge detection operators, the P-M diffusion on real domain will produce "ladder effect", so we expand it to complex field, use the imaginary part as edge detection operator, solve the problem.This paper introduced Coherent Enhancement Diffusion of Anisotropic Nonlinear Diffusion Model. The Coherent Enhancement Diffusion can enhance image edges, make some of the fracture linear structure repaired, but because of the noise impact, the image smooth area will create many false stripe. This article, in view of the characteristics of P-M and Coherent Enhancement Diffusion, makes two models together. Firstly, we use the Canny Edge Detection Operator to do the area segmentation, then in the edge regions with Coherent Enhancement Diffusion, the non-edge regions with P-M Diffusion. According to this principle, this paper put forward Based on Weighted Mixed Diffusion and Based on Image Segmentation and Fusion Technology Mixed Diffusion, used the two kinds of mixed model to process the image contained noise.This paper also discussed the partial differential equations of the image enhancement. Backward diffusion equation has the image edge enhancement effect, but with the iteration, the process will produce oscillation and make the image information lost, so this paper combined with the forward diffusion and backward diffusion. It can denoising, in the meantime, can enhance the edge, and also inhibit the oscillation of happen. Then we expand the forward and backward diffusion from real domain to complex field to avoid the flat area "ladder effect". In order to increase the equation ability to remove noise, we combined the P-M diffusion and forward and backward diffusion, sharpening edges and filtering out more flat area noise.