| Image denoising, which is the foundation of other subsequent image processingproblem, is one of the most basic problems in digital image processing. It means alot in the domain of both theory and application. Since1990s, image denoisingmethod which is based on partial differential equations has been developed.Compared with the classic ones, it has a better the oretical foundation and steadyarithmetic.In the first part we present the research background and current situation ofimage denoising and the mathematical model of of the traditional image processingfilter. In this dissertation, we use the nonlinear partial differential equations. In thesecond part, we introduce the PM model for image denoising. We present theparticular of the process of the model and analyse its characteristic. By means ofpresenting the computational result, we find the disadvantage of PM model, that iseasy to loss of edge information. In the third part, we find the disadvantage of ROFmodel, namely the effect of staircase. In this dissertation, our improvements arepresent as the following two aspects.Firstly, we present two new diffusion coefficients which can improve thefourth-order partial differential equation method.By introducing the fourth-orderpartial differential equation method which can remove the staircase effect we find itsdisadvantage: its computational result shows the existence of some isolate dots. Tosolve this problem, We develop two different new diffusion coefficients which canremove isolate dots. The computational results show that both coefficients performwell in reducing running time.Secondly, we develop a new composed method which takes advantage of thevariational methods and the new fourth order partial differential equations. Thecomputational result shows the good performance of the composed method, whichuse the second diffusion coefficient. The new method has less running time andhigher Peak Signal to Noise Ratio (PSNR), which is proved to be a successfulmethod. |
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