Image Denoising Based On Partial Differential Equation

The noise removal of image has always been a popular issue in the field ofimage processing, it is also the preparation of image processing applications.Traditional methods of image denoising could destroy the image features such asedge, line, texture. The algorithm based on PDEs could keep details of the imagefeatures, while restoring image. So it is becoming more and more attracted.For the basic problem of the noise removal of image, with the method ofimage modeling, this thesis has mainly discussed two different types of modelsof the noise removal of image from different angles: The first one is the model ofnoise removal based on scale-space axiom system, it has mainly discussedanisotropic diffusion equations according to direction filter. The second one isthe model of PDEs, it has mainly discussed total variational model and four orderpartial differential equations, which are widely used.In this paper, the improvement is: (l) According to the nature of scalespace,this paper shows the method how a class of linear PDEs be derived andgives the Matlab program of the Extreme killer operator, based on level set. (2)Since the two order PDEs is designed such that smooth areas are diffused fasterthan less smooth ones, blocky effects will appear in the early stage of diffusion,the use of fourth-order PDEs as a technique to avoid blocky effects whileachieving good trade off between noise removal and edge preservation, But noisehas not been completely removed by fourth-order PDEs. We change the diffusioncoefficient of the two models. According to the comparison of the two newmodels, this paper proposes a combined model which combines two order PDEsmodel and four order PDEs model by weight function. The experiment showsthat the combined model not only can overcome the shortcomings of the twomodels, but also can integrate their advantages. It has better performance indenoising, protecting smooth areas, protecting the edge and texture details. Thispaper also gives a variety of tests to prove the superiority.