Weighted Minimization Of Matrix Singular Values For Image Denoising

Image denoising is a hot issue in image processing.How to remove the noise in the damaged image and preserve the original information as much as possible has attracted the attention of researchers.Recently,denoising algorithms based on low-rank matrix approx-imation have been widely used in image processing due to their excellent image denoising performance.Low-rank matrix approximation can generally be divided into low-rank matrix decomposition methods and nuclear-norm minimization methods.As the tightest convex re-laxation of matrix rank,nuclear-norm minimization has extensive research and application in solving low-rank matrix approximation problems.Inspired by the Schatten-p norm,this paper proposes a more flexible Multi-channel Weighted Schatten-p Norm Minimization(MC-WSNM)optimization model for RGB color image denoising based on the framework of the Multi-channel Weighted Nuclear Norm Minimization(MC-WNNM)model.Using the alter-nating direction multiplier method(ADMM)framework and the generalized soft threshold algorithm(GST),the optimal solution of the optimization model can be effectively obtained.Applying the MC-WSNM model to the color image denoising,almost the highest PSNR in-dex value and excellent intuitive visual effects can be obtained in both the synthetic noise image experiment and the real dataset experiment.On the basis of the MC-WSNM model,considering that there are not only Gaussian noise but also other noises in practical applica-tions,this paper proposes an extended MC-WSNM model based on noise prior information.This model uses the Lq(1 ?q?2)norm of the matrix as the data fidelity term instead of the Frobenious norm.To solve the optimal solution of the model effectively,the alter-nating direction multiplier method is used to optimize it,and then the optimal solution of the model can be obtained effectively through the generalized soft threshold algorithm and the proximity operator.It is worth noting that the MC-WSNM model is a degenerate form of the extended model for removing Gaussian noise when p=2,which can also be used to remove impluse noise by setting p=1.The experimental results show that the L1 norm data fitting model can result in better performance compared with the Frobenious one in impul-sive noise.Therefore,the extended Multi-channel Weighted Schatten-p Norm Minimization optimization model is more generalized.