| Image denoising, which is the foundation of other subsequent image processing problem, is one of the most basic problems in digital image processing. It means a lot in the domain of both theory and application. Since 1990s, image denoising method which is based on partial differential equations has been developed. Compared with the classic ones, it has a better theoretical foundation and steady arithmetic.In the first part we present the significance of image denoising and the mathematical model of noise in an image. We introduce some classic methods of image denoising. In this dissertation, we use the variational methods together with partial differential equations. In the second part, we introduce the ROF model for image denoising. We present the particular of the process of the model and analyse its characteristic. By means of presenting the computational result, we find the disadvantage of ROF model, namely the effect of staircase. In this dissertation, our improvements are present as the following two aspects:Firstly, we present two new diffusion coefficients which can improve the fourth-order-partial-differential-equation method. By introducing the fourth-order- partial-differential-equation method which can remove the staircase effect we find its disadvantage: its computational result shows the existence of some isolate dots. Then we analyse the reason. We develop two different new diffusion coefficients which can remove isolate dots. The computational results show that both coefficients perform well in reducing running time and increasing the Peak Signal-to-Noise Ratio (PSNR).Secondly, we develop a new composed method which takes advantage of the variational methods and the new fourth order partial differential equations. The computational result shows the good performance of the composed method, which use the second diffusion coefficient. The new method has less running time and higher PSNR, which is proved to be a successful method. |
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