Research Of Partial Differential Equation Model In Image Denoising

The paper firstly analyzes the significance of research, the development of history of the image processing based on partial differential equation. And expounds the mathematical theory knowledge of image denoising. Finally, introduces a shock couple diffusion model for multiplicative noise removal, multiplicative noise removal model based on nonlocal regularization. It mainly includes the following contents:The paper firstly introduces the research background and significance of topic selection in chapter 1, then expounds the development history of image denoising algorithm based on PDE.In chapter 2, it introduces the concepts and other basic knowledge related to image denoising, mainly includes the classification of the noise model, evaluation criterion of the model, variational method and gradient descent flow, the numerical calculation of finite difference method and the basic idea of image denoising.In chapter 3, it describes some classic model of image denoising, including P-M diffusion model, ROF model and fourth-order YK denoising model of additive noise removal;and AA model, Log-TV model, SO model of multiplicative noise removal.Then discusses the advantages and defects of all kinds of denoising model.A shock couple diffusion model for multiplicative noise removal is presented in chapter 4, by taking a logarithm transformation for multiplicative noise model, it can be converted to the additive noise model, this chapter applys the ideas of removal additive noise of P-M diffusion model to removal the multiplicative noise model. It defines a new diffusion velocity function in the model, and modifies the selection of controlling control parameters. Compared with classic denoising model results and then compare the extracted edge information of the image, the experimental results demonstrated the effectiveness of denoising. The proposed denoising model can preserve edges and suppress the “staircase effect”.A general multiplicative noise removal model based on nonlocal regularization and Split-Bregman algorithm is presented in chapter 5. Combining with the removal multiplicative noise Log-TV model, some improvement can be made. The nonlocal TV norm, ie.NLTV, is chosen during the regularization of the model. The smooth degree of the model is determined by the image gray similarity between the regions, which can keep the image texture structure. The Split-Bregman algorithm is applied to solve the model. Finally, compared the experimental results with Log-TV model. Experimental results demonstrated the effectiveness of the model.