Noise Image Restoration Algorithm Based On Total Variation Regularization Model

Image restoration,as an important inverse problem,has been studied for a long time and is still a challenging problem.In the process of image restoration,it is difficult to find a stable solution to obtain a clear image.The optimization model based on total variational（TV）regularization has been widely studied as an effective method.The main work of this paper is to study the TV model and build corresponding models to solve the pulse noise and Gaussian noise in the image respectively.The main tasks are as follows:Firstly,the research significance of image restoration algorithm and the research status of image restoration in transform domain and spatial domain are introduced in detail,and the theoretical knowledge of TV regularization model and non-local regularization,as well as the principle of compressed sensing（CS）and the construction of common measurement matrix are studied and analyzed.Aiming at the solution of TV regularization optimization model,the concrete process of splitting Bregman algorithm and ADMM algorithm is introduced.Finally,the objective evaluation indexes commonly used in the process of image restoration are studied.Secondly,the impulse noise image restoration model is constructed based on TV regularization model,with l₁ norm as data fitting term and gradient operator and wavelet frame as regularization term.The split Bregman iterative algorithm and ADMM algorithm are used to solve the model,and the convergence of the model is proved.Standard experimental images and simulation images were selected to add 10%,20%and 50%pulse noise respectively to verify the restoration effect of the model.Combined with PSNR,Re Err and SSIM,this method was compared with other methods to prove the universality and effectiveness of the proposed model algorithm.Thirdly,for gaussian noise in images,a gaussian noise image restoration model based on TV regularization is constructed.The advantages of compressed sensing and non-local self-similarity in noise image processing are utilized.Based on l₁ norm,sparse optimization and non-local regularization are regarded as regular terms.The split Bregman iterative algorithm and ADMM algorithm were used to solve the model.Standard experimental images and simulation images were selected to add some Gaussian noise respectively to verify the restoration effect of the model.At the same time,the compression ratio of measurement matrix in CS theory was adjusted to discuss the influence of different compression ratio on the restoration model.Experimental results show that the proposed restoration model can effectively suppress the step effect of smooth region,protect the details of image edge,and perform better in Re Err,SSIM and PSNR values.