| Of all the medias for human being getting information ,the most important is image. Noisein image is inevitable because of image acquirement, equipment and transmission. How toremove and degrade it has been becoming a constant research topic in the fields of imageprocessing. In recent years, variational partial differential equation (PDE) method in imageprocessing has received extensive concern. Compared with other approaches, variational PartialDifferential Equation method has remarkable advantages in both theory and computation, and itcan profoundly benefit from the existing wealth of literature on numerical analysis andcomputational PDEs.Firstly, this article has introduced concept of the digital image and the processing, analyzedthe significance of image denoising, studied domestic and foreign present situation about imagedenoising based on the partial differential equation and given the assessment methods of imagedenoising.Secondly, this thesis has proposed development of the partial differential equations in theaspect of image denoising, given several kind of typical diffusion equations and carried on theexperiment to analyze its nature, pointing out its merit and insufficiency.Finally, image denoising with P-M diffusion often leads to an undesirable "staircase"effect, so we have used gradient fidelity item to eliminate this very insufficiency. In order tomaintain the edge information while denoising, we needs to use the highly non-linear partialdifferential equation model, but this directly causes "staircase". This paper first reviews theformer methods of "staircase" and introduces gradient fidelity term in the diffusion equation.This model can maintain the gradation of the processed image the same as the original image,thus preventing the "staircase" effect. Because this denoising model maintained the low-ordernon-linearity diffusion equation form, it can get more simple and stable digital solution,compared with higher-order partial differential equation denoising model.
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