The Image Denoising On An Implicit Open Surface Based On Variational Method

Noise removal is one of the fundamental tasks of image restoration which can get clear images from the corrupted ones by different noises.In recent years, the image diffusion based on variational method has become the main method in image denoising. It’s main idea is that the image is converted into the energy functional and the diffusion equation is received,and then we seek the minimum.Such method has been widely used in image diffusion about plane and the implicit surface. Based on the concepts of intrinsic gradients, intrinsic divergences and using the intersection set of zero level set of a signed distance function and a characteristic function to express the implicit open surface, a varaitional model of image denoising on an implicit surface is proposed.The image diffusion on an implicit open surface is deeply discussed in this paper, and some solutions to existing problems are put forward. And several aspects are introduced as follows:Firstly, the image diffusion based on variational method and the theory about implicit surface is studied. Secondly, Split-Bregman algorithm transforms original variational models into solutions of simple Poisson equations and generalized soft thresholding formulas by introducing auxiliary variables. In this way, the calculation speed of variational models is improved. Moreover, Bregman iteration speeds up the convergence rate of energy functional and enhances restoration quality. Thirdly, according to the characteristics of image diffusion on implicit closed surface model and its relationship with the open surface, a general varaitional model of image denoising on an implicit surface is proposed, which includes a data term and a regularization term. the regularization term can be TV (Total Variation), PM (Perona and Malik) and TV-L1regulerizers. The model is tested through numerical experiments on different combinations of data terms and regularization terms.