Variable Split Points Image Diffusion Tv_l1 Model Calculation

Image restoration based on variational method and PDEs is One of the major schools of computer vision and image processing fields.These methods define an energy functional first,and then obtain the PDEs throw variational method,and get the solution by solving the PDEs at last.The main defection of the methods is inefficient.In order to make the implement simple and efficient,this paper introduced one or more auxiliary variable into the energy functional.And the energy functional based on first order or second order then split into several simple energy functional.The paper's work includes the following aspects: firstly,we studied the TV models based on gradient and based on divergence in detail.The Euler-Lagrange equation,diffusion equation,Gradient descent equation and iterative scheme are obtained by variational method and finite difference of the equations.A hybrid variational image diffusion model using gradient and divergence is presented in this paper to reduce staircasing during image diffusion with edge preserving or enhancement.Secondly, the paper solving the TV models using splitting methods.The paper proposed two splitting methods to solving TV modes:anisortropy approximation and isotropy approximation. Thirdly,in order to solving the TV_L1 models,the paper also proposed two splitting methods:anisortropy approximation and isotropy approximation.Fourthly,established a hybrid variational image diffusion model using gradient and divergence of TV_L1,and proposed a splitting method to solve it.