Image Restoration Method Based Wavelet Framework For Removing Cauchy Noise

Digital image processing plays a major role in real life,and modeling im-age recovery using mathematical knowledge and designing efficient algorithms for processing is a common approach in image processing today.By studying digital images corrupted by both noise and blur,an optimal model is designed and an ef-ficient algorithm is used to solve the model.This paper focuses on how to remove the Cauchy noise and blur,from model building,algorithm selection to solution,and convergence analysis.The main contents are as follows.1.With the theoretical knowledge of compressive perception,we propose a non-convex regularization model with Cauchy noise removal and blurred images.The model consists of two main parts,one for the data fidelity term with Cauchy noise removal and the other for the regularization term based on the weight dif-ference between the7)₁parametrization and the7)₂parametrization of the wavelet framework.We solve the model using the convex function difference algorithm（DCA）and the alternating direction method of multiplier（ADMM）.And the con-vergence of the two algorithms is proved.The experimental results show that our proposed method has significant advantages over other methods for removing the Cauchy noise.2.Since the sharpening operator of the image is considered to highlight the detail information and the median filter can effectively remove part of the noise,we process the degraded image by these two methods and introduce the processed result as a preprocessing7)₁-norm term into our model,which is used as a canonical term together with the7)₁-norm based on the wavelet framework,we obtain the preprocessing to remove the Cauchy noise and blur model.We use the alternating direction method of multiplier to divide the model into several subproblems for solving,and our model is more efficient compared with related methods.3.Since it is possible that in real-life images there is not only the same kind of noise,we consider the case of simultaneous existence of the Cauchy noise and Gaussian noise,and we propose a non-convex model with simultaneous removal of mixed Gaussian Cauchy noise and blurring by using the7)₁parametrization with wavelet as the framework as the regular term and the data fidelity term as the summation term of Gaussian and Cauchy noise.The alternating direction method of multiplier is used to solve the model,and convergence analysis is given.In our experiments,we recover for color images,and since there are few existing methods for removing mixed Gaussian Cauchy noise,we add convex variational methods to Gaussian noise and compare them,and the data indicate that our method is still effective for processing color images.