An Improved Algorithm Of Partial Differential Equations Based Regularization Smoothing Method

Images are important methods by which people access information. But there existsvarious of errors when images are collected, acquired, encoded, stored and transmitted,such as optical diffractive errors, nonlinear aberration of sensors, disturbed effects byatmosphere convection, blur introduced by image motion and geometric aberration.All these errors will influence people to access the correct information. So varioustechnical methods are necessary to process images. Among all these methods imagerestoration is an important one. It is used to improve the quality of images.Image restoration processing is to rebuild or restore original images with somepriori knowledge according to given degraded images or noise-polluted images. Thereare some classical methods: inverse filtration, Wiener filtration, mid-value filtration,Gussian filtration,etc. But all these methods will blur edges, lines, textures and otherimage features. At present, the methods based on partial differential equations (PDE)are been studied to solve these problems. Image regularization based on partial differential equations is used to removeunnecessary image features while keeping interesting ones. The regularizationmethods based on PDE can be considered as a nonlinear filtration. They simplifyimage data by some method to keep only interesting image features. The anisotropicdiffusion methods based on PDE can keep image features such as edges, lines andtextures while removing noises.In this paper we summarize the regularization methods based on PDE and proposea pair of new image smoothing functions. The function of image regularization can beexpressed as a minimization of energy function of image variance metrics. It can besolved by iteration of gradient descent. This iterative formula is an equation based ondiffusion and can be transferred to a formula based on trace; at the same time, it canbe reduced that a directive Laplacian operator can also be expressed a formula basedon trace. So we can use the convolution of Laplacian operator to compute the gradientdescent. A general formula based on trace equation is been used to unify threedifferent regularizations. Finally we give a pair of new image smoothing functions.The image processing algorithm based on these functions can keep image edges whileremoving noises and it can avoid block effects introduced by other PDE methods. Theexperimental results show a high quality of image restoration.