Research On Variational Multiplicative Noise Removal Models With Variable Exponents

Noise removal in images is an important and difficult technique which is the premised preparation of most work in images and it needs to make higher level of the accuracy.The techniques of noise removal in images based on partial differential equations have been mature which have got the interesting of professional scientist and made a great progress,some of which based on variational approach for multiplicative noise have performed outstanding achievement and laid the functions of future study.In this paper,the main research is to present the variational multiplicative noise model with variable exponents,next to prove the existence and uniqueness of solutions of model and the comparison principle,then to prove the existence and uniqueness of solutions for evolution equation and its related properties.Finally,we give the experimental results of model and the acceleration algorithm and compare with the classical model.We remove multiplicative noise based on variational methods in this paper.The features of Gamma noise model are different form standard Gauss addictive noise by the way of how they produce.Firstly,in the paper,inspired by the variation multiplicative noise model of Dong,et al,we improve the term of regularization by using gray levels and module of Gauss gradient,then construct the variable exponents of the regularization term which between the exponents of total variation and 2L regularization term.At the same time,it can suppress the staircase effect,adaptively remove noise,and protect boundary and information of images.In theories,under the framework of variation models with variable exponents for multiplicative noise removal,we prove the existences of the minimizer problem for the model by turning it into the existence of minimizer of functions and the uniqueness of that by strong convex of functions.Then,we prove the comparison principle by the existence,uniqueness and natures of spaces.In terms of relevant evolution equations,firstly,we define the anisotropic Sobolev spaces with variable exponents for the definition of weak solution.Our regularization method in equations can overcome the degeneration.A prior estimate on solution can solve problem of the singular points.Then,we approach the limit of regularized equations under the definition of weak solution and prove that the limit satisfies the definition of weak solution of evolution eq uations.Finally,we prove the existences of the weak solution.As for the uniqueness and the comparison principle of the weak solution,it can be proved by the nature of equations and variety of Gronwall inequations.Numerically,we show the discrete finite difference scheme.Next,we implement it by the method of finite difference and fast explicit diffusion(FED)on M ATLAB.We also compare it with other tradition methods and analyze results in experiment.Finally,the experimental results illustrate FED improve the effectiveness of the algorithms of the model,which is superior to traditional multiplicative noise removal methods on the time and performance in experiments.