Research On Mathematical Model And Fast Algorithm Of Image Denoising

In the information age,images have become an indispensable way to obtain information.In order to facilitate statistical analysis before acquiring images,many image processing problems are often involved.Image denoising is usually done before higher level image processing,which is the basis of image processing.There are many way to source noise.The noise types are also different,and each noise has unique statistical and structural characteristics.These noise severely damages the visual effects of the original image and hinders subsequent analysis of the image.Therefore,image denoising is a basic and necessary research question.In engineering applications,image noise is often approximated by Gaussian noise.We mainly studied two types noise in practical applications: Cauchy noise in medical images and stripe noise in remote sensing images.The regularization method is the basis of this study.By deeply analyzing the statistical characteristics of the Cauchy noise in the medical image and the structural characteristics of the stripe noise in the remote sensing image,exploring the prior information of the image,and pointing out the defects of the current research work,we propose a new regularization model and design an effective algorithm to solve the proposed model,respectively.The effectiveness and superiority of the proposed method are demonstrates in terms of theory and numerical experiments.The main research contents and innovations are as follows:First,we propose a new regularization model for removing Cauchy noise.The model combines total variation(TV)and high-order TV,so that the optimization model can maintain the edge information of the image while maintaining the smoothness of the restored image in a uniform region.We introduce a strategy to adaptively select regularization parameters,so that the regularization parameters and the restored image can be optimized simultaneously.In addition,we design the alternating minimization algorithm to transform the non-convex problem into two simple convex problem with guaranteed convergence.Experimental results demonstrate that the proposed method has the advantages of better preserving edges and removing the Cauchy noise.Second,we propose a novel regularization model for stripe noise removal.By exploring the directional and low-rankness of the stripe noise,the proposed model applies TV and the unidirectional high-order TV to constrain the smoothness of the image,and uses the Schatten 1/ 2-norm to characterize the low-rankness of the stripe noise.We design an efficient alternating direction method of multipliers algorithm to solve the proposed model,and the proposed algorithm can effectively separate the potential image and stripe noise.Extensive experiments on synthetic and real data are reported to show the superiority of the proposed method over state-of-the-art methods in terms of both quantitative and qualitative assessments.