Research On Image Denoising Based On Fractional Order Partial Differential Equation

With the development of the human society and the science technology, the digital image processing has been widely applied to various fields, from the very beginning of the aviation industry and the information of communications to modern industry, biology, medicine of agriculture, intelligent robots industry and many other aspects. Noise interference in the process of transmission and acquisition of digital images reduces image quality and influences subsequent processing, such as image compression and image segmentation. Denoising algorithms are commonly used in digital image procession, including mean filtering, low-pass filtering and Wiener filtering, etc. However, when the algorithms mentioned above are used to suppress noise, fuzzy processing is taken to the edges of images.The preservation of the detailed information and the removal of the noise information is a contradiction that can not reconcile in the denoising processes. The traditional denoising algorithms would undermine the image edge, texture and other details when removing noise. The denoising algorithm based on partial differential equations, which can make selective smoothing for the image, and it is able to resolve this contradiction perfectly. The partial differential equations image denoising model was researched by the combination of theoretical analysis and simulation experiments in this paper. The main research work of this paper is divided into the following contents:Several classical image denoising methods based on partial differential equations are introduced, Analyzing these models and summarizing their advantages and disadvantages. On the basis of total variation denoising model, and two new improved models are proposed. In this paper,doing the simulation experimen for the above denoising models by MATLAB tool. And, analyzing the experimental results by subjective and objective evaluation methods of the image quality.(1) By combining fractional differential operator which can enhance image texture information with variational partial differential equation and then applying to image denoising. A denoising model based on fractional partial differential operator is put forward. The model can not only better suppress noise of the image, but also better preserve detailed texture information. However, the order of the fractional differential operator must be determined by a lot of experiments. Therefore, calculating local variance is chosen to express the complexity of the local image texture so as to realize adaptive determination of the order of fractional differentiation.(2) For disadvantages of the fidelity term can blur the image edge. Proposing the algorithm which combine the gradient fidelity term with fractional-order anisotropic diffusion. Introducing the concept of local gradient fidelity, so that weighted the gradient fidelity term, use algorithm of gradient fidelity term for denoising in the part of image smoothing region, and use fractional-order partial differential equations for denoising in the edge region of the image.