Study Of Image Denoising Model Based On Regularization Method

Image denoising is an important issue of image processing as the degraded image can cause a lot of limitations for further application. Mathematically, image denoising is an inverse problem, and it will be an ill-posed inverse problem if there is a blur kernel. At present the most important and effective way of solving inverse problem is regularization method. The main idea of regularization method is that take regularization operator as the approximation of the original ill-posed operator, the regularization solution is the approximation of the original ill-posed problem solution. The regularization solution is unique and stable. For image denoising, main regularization methods are Tikhonov regularization and total variation regularization. There are harmonic model based on Tikhonov regularization and TV model based on the total variation for PDEs model of image denoising, both of them have advantages and disadvantages. So, in this paper the adaptive total variation model(ATV) is studied, which effectively combines harmonic model with TV model. Details are as follows:The method of image denoising based on PDEs often use variational method and the heat conduction theory, therefore, this paper does a more detailed description for these two method, mainly proves the famous Euler-Lagrange equations, analyzes the process of heat conduction isotropic diffusion and anisotropic diffusion.From the perspective of the inverse problem, regularization method is an effective way to denoising. Relevant researches on Tikhonov regularization method and total variation regularization method are done, and more detailed description of these two regularization theory are given. The image denoising method based on harmonic model is an isotropic diffusion method, from the experiment of digital image denoising, you can see it has obvious advantages and disadvantages, which have a good effect on image noise suppression, especially for the smooth areas, but it blurs the image edges and details; on the contrary, the image denoising method based on TV model is an anisotropic diffusion method. In this paper the experiments of digital image denoising using the method of TV model are also made, and the experiments show that its denoising effect is better than harmonic model, which retain the image edges and details but there are clear "ladder" effects.Harmonic model based on Tikhonov regularization uses2-norm, and TV model based on the total variation regularization uses1-norm, in order to effectively make use of the advantages of these two image denoising methods, an adaptive total variation model based on p-norm is proposed. Two research ideas for this model are given:the first is setting the values of p-norm depend on the total variation of the image, the second is setting the values of p-norm depend on the edge detection. In this paper edge detection based on Laplacian operator is proposed to determine the value of p-norm, and a comparison test with harmonic model and TV models is done. Test shows that the denoising effect of this method is significantly better than the previous two methods. In this paper an experiment of p-norm values depending on total variation of the image is also done and experiment shows that it’s denoising effects is nearly the same with p-norm values depending on edge detection based on Laplacian operator.