Research On Denoising Integrated Model Of Partial Differential Equations

Digital image, one of medias transmitting information, has been widely adopted by its objectiveness and conciseness particularly in the information revolution age. However, the quality of image vision has always been affected seriously such that the succeeding analysis and processing become a difficult task which is because "the noise" occurs in the process of forming, conveying and transforming of image when the image sensors are interfered by various factors. Nowdays, digital image processing technology has developed into a subject. So the image denoising has become an important part in the image processing which directly affects the results of subsequent processing and analysis.Partial differential equations (PDE) image denoising model was researched from aspects of principle analysis, simulation and experiments. The paper is divided into five chapters. In chapter one the research background and significance are described, the history of PDE image processing and the current research situation are summarized, the ideas and methods of this paper are given. In chapter two the concept of digital image processing and classification, the mathematical model of the noise image, classification and denoising evaluation criterion are introduced, and several conventional methods of filtering noise are reviewed. In chapter three the modeling principles of PDE denoising model are expatiated, and several typical PDE denoising model are analyzed. The main attention is put on the chapter four and the chapter five. In chapter four, we analyze the total variation (TV) denoising model in which the image edge can be remained, but the filtered image has a "massive effect", and the fourth-order PDE denoising model in which the "massive effect" can be eliminated in flat areas but in smooth areas the filtered images easily has uneven region phenomenon. The first integrated model based on analyzing the PDE image denoising above is proposed, which remains the advantages of the TV denoising model and the fourth-order PDE denoising model and deposes their disadvantages. The first integrated model is also improved when we apply composed filter methods to remove the bright spots. MATLAB simulation results show that the result of the first integrated model is better than other models. The model takes into account effectively both noise removal and protection to the image edge details. It is regret that the first model does not remove the salt and pepper noise. On the basis of chapter four, the second integrated model is proposed in chapter five which can effectively remove the salt and pepper noise. Experimental results show that the two integrated models have certain advantages such as making the filtered image close to the original image,and effectively removing the noise.