Image Denoising Model Based On Four-direction Total Variation

Image denoising is an important basic research topic in image processing.It is a previous work for edge detection,image segmentation,image registration and so on.Total variation(TV)denoising model has been found wide applications in image processing,since it can preserve the edges well.However,it can easily make the smooth transition region of the image become the constant,which brings about the staircasing effect.Therefore,some improved models have been proposed by many researchers.TVP model is one of them,which combines the advantages of the L2 model and the TV model.It can not only remove the noisy,but also give consideration to preserving both the edges and the smooth region,so it can reduce the staircasing caused by the TV model in some degree.Generally speaking,the solution of the variation model is difficult,therefore,the proper discretization method can help to find the numerical solution of the model.Nowadays,there are two numerical solution patterns,one is using the optimization method for the discretization model(namely discretization-optimization),the other is using the discritization method for the Euler-Lagrange equation obtained by the variation model(namely optimizationdiscretization).In this paper,firstly,a new four direction TV model is constructed by using the four pixels in four neighborhood domain of the pixel to discrete the regularization of the TV model.Secondly,the gradient modulus of the Euler-Lagrange equation obtained by the TVP model is discretized by the new four direction.The major works are as follow:1.A new four direction TV model is constructed by using the forward and backward difference of the gradient in each pixel points to discrete the regularization term of the TV model.A nonlinear equations are obtained by the optimization method,and then a fixed point method with lagged diffusion coefficient is proposed to solve the nonlinear equations.Finally,A comparison between our model with TV model,the four direction TV models for isotropic and anisotropic is made.Test data show the signal-to-noise ratio obtained by our model is obviously higher than the other models,the cost of the time and the number of iteration steps for our model is the least of all.Observed by the restored images,we can draw the conclusion that our new model can keep the edges as well as the TV model,and it can also efficiently reduce the staircasing.2.The nonlinearity of the Euler-Lagrange equation obtained by the TVP model is so high that it is difficult to solve.A proper discretization scheme which is designed by using the geometric mean for the forward and backward difference of the gradient in each pixel points is proposed for discretizing the gradient modulus of the Euler-Lagrange equation to deduce the nonlinearity of the Euler-Lagrange equation.Example data show that the convergence of the lagged fixed point method is faster by using the proper discretezation for |▽u|,and the signal-to-noise ratio of the restored image is obviously improved by using the proper discretezation for |▽z|.