A High-order Variational Model And Its Fast Algorithm For Color Image Multiplicative Noise Removal

Image noise is generated during transmission or storage.According to the relationship between image noise and image signal,it can be divided into additive and multiplicative noise.In recent years,many variational models for removing additive noise have appeared.However,the multiplicative noise existing in the color image cannot be removed well.In addition,the traditional low-order model has defects such as step effect,contrast imbalance,blurred edges or missing corners when removing noise.Therefore,it is necessary to further study the high-order model for removing multiplicative noise of color images.Due to the need to consider the coupling relationship of color image layers,the variational denoising model of grayscale images cannot be directly used for color image denoising.The high-order variation model for removing multiplicative noise of color images proposed in this thesis is mainly divided into M-TGV(Multi-channel Total Generalized Variation)model,M-Euler-elastic(Multi-channel Euler-elastic)model and M-TC(Multi-channel Total Curvature)Model.Due to the complicated solution process and long operation time when the traditional solution method is used to solve the higher-order model,this thesis introduces the corresponding auxiliary variables,split Bregman iteration parameters and Lagrange multiplier when solving different models,using the fast Fourier transform,generalized soft threshold formulas,projection method and other methods,and design a fast algorithm corresponding to the model.Use split Bregman algorithm to process M-TGV model and M-Euler-elastic model,and use augmented Lagrangian algorithm to process M-TC model.The results of the three models proposed in this thesis for different multiplicative noise images are compared with the denoising results of the traditional CTV model and MTV model.The final conclusion: From the qualitative perspective,the three models proposed in this thesis can effectively remove the staircase effect,and can better maintain the edges,corners,and details of the image;From a quantitative point of view,the peak signal-to-noise ratio of the image and the structural similarity index of the image after denoising are higher than the CTV model and MTV model.The convergence speed and operation time of the model are improved,which verifies the advantages of the model in this thesis to remove multiplicative noise of color images.