Study On Algorithm Of Image Denoising Based On Partial Differential Equation

Image processing based on partial differential equations began in the 1990s, and for decades, many mature and highly efficient algorithms based on the P-M model have been proposed through the tireless efforts of many experts and scholars, for example, the Catte model, Alvarez-Lions-Morel model, Total Variation (TV) model and so on. These models are widely used in image restoration, image segmentation, image reconstruction, image analysis and so on. As a classic area of research, the key of image denoising is to remove the noise, and retain the important features, such as image edges, of the image at the same time, and to minimize the impact of subsequent image processing from noise as far as possible. This paper made a more depth study on image denoising based on partial differential equations, and two new image denoising models are given, which have achieved the ideal denoising in the simulations. This paper is organized as follows:The chapter one describes the subject background, significance and the current research situation, the relations of PDE and functional variation. In chapter two, the basic knowledge of digital image processing are briefly summarized, including digital image classification, noise models, the subjective and objective denoising evaluation criterions, and two conventional methods of filtering noise. In chapter three, several classical image denoising methods based on partial differential equations are introduced. The main work is the chapter four. Two new image denoising models are proposed, we get the first model with weighted function, based on both the isotropic diffusion model and the Total Variation (TV) model, and this new model inherits the advantages of both and makes up their disadvantages, such as removing the noise effectively and retaining the image texture and edge information. According to the characteristics of the second-order equation and the fourth-order equation, we proposed the second new model. In the flat areas of the image processing, this model plays the role of the second-order equation, accelerating the smooth and protecting the edge in the regional area. In the gradient region of the image processing, it plays the role of the fourth-order equation, protecting the details. Compared with the other models, simulation results show that the denoising results of the new models have a lot of progress. However, the situation of the noise is more complex in practice than in the simulations, therefore, many denoising methods should be used when we want to get a more ideal performance. In chapter five summary and outlook are described.