Research On Image Denoising Algorithm Based On Statistical Analysis And Tensor Decomposition Model

Image is the visual source of human perception of the world.It is an important way for human to obtain,express,analyze and transmit information.With the rapid development of modern multimedia technology and artificial intelligence,the camera lens has penetrated into all aspects of human social life,and the digital images generated every day show exponential growth.However,the image in the process of acquisition,coding and transmission is inevitably affected by noise.Noise not only damage the image quality,but also directly affect the effect of subsequent image processing,such as target recognition,target tracking,etc.Therefore,in order to obtain high-quality digital image,it is necessary to denoise the degraded image,and retain the original image information from the observed noisy image as much as possible to remove the noise.In this paper,from the point of view of statistical analysis and tensor decomposition,the image denoising problem is deeply analyzed by using the low rank characteristics and sparse representation of images.The main work of this paper is as follows:1.The nonlocal self-similarity(NSS)prior of images has been successfully used in many image denoising methods.Most of the existing image denoising methods only consider the NSS prior information of the given noisy images or natural images.How to exploit the information of both external natural images and the given noisy image to achieve better denoising effect has attracted our attention.Patch groups are extracted from natural images by putting nonlocal similar patches into groups,and a PG based Gaussian Mixture Model(PG-GMM)learning algorithm is adopted to learn external priors from an independent set of clean natural images.With the aid of external priors,we then learn internal priors from the given noisy image to refine the prior model.We demonstrate that,owe to the learned PG-GMM,a simple weighted sparse coding model can be used to perform image denoising effectively,resulting in high image denoising performance.2.We treat real-world noisy images as third-order tensors with column,row and color modes.Considering two inherent characteristics of a color image including the nonlocal self-similarity(NSS)and the cross-channel correlation,we extract non-local similar patch groups from a color image and treat these groups as tensors with each color channel corresponding to the frontal slice of the tensor to exploit the information within and cross channel correlation.Inspired by recently proposed tensortensor product(t-product),t-SVD,tensor tubal rank and rigorously deduced tensor nuclear norm,a novel t-product based weighted tensor nuclear norm minimization(WTNNM)is proposed to model the extracted non-local similar patch group tensor(NPGT).Considering the NPGT is of low tubal rank,we formulate real color image denoising as a low tubal rank tensor recovery problem and solve it with the weighted tensor nuclear norm minimization.Experiments on both simulated and realistic noisy images verify the effectiveness of our method.3.To fully exploit the spatial and spectral correlation information,we present a new real color image denoising scheme using tensor Schatten-p norm(t-Schatten-p norm)minimization based on t-SVD to recover the underlying low-rank tensor.Similar to matrix Schatten-p norm,using non-convex t-Schatten-p(0 < p < 1)norm minimization could obtain better results than the tensor nuclear norm minimization which is a convex relaxation of the nonconvex tensor tubal rank.To avoid overshrink the tensor tubal rank components,a flexible weighted t-Schatten-p norm model is proposed with weights assigned to different elements of tensor singular tubes.We adopt the generalized iterated shrinkage algorithm to solve the minimization problem efficiently.Extensive experiments on one synthetic and two realistic datasets demonstrate the effectiveness of our proposed method to remove noise both quantitatively and qualitatively.4.The proposed real color image denoising scheme using tensor tubal sparsity regularization method exploits two intrinsic characteristics of a color image including the nonlocal self-similarity(NSS)over space and the correlation across color channels,thereby both the spatial and cross-channel correlation information within the nonlocal similar patches can be fully utilized.We adopt the tensor tubal sparsity to characterize the nonlocal patch group tensor(NPGT)and exactly recover the clean data by solving the tensor tubal sparsity optimization problem.We learn the dictionary adaptively from the given noisy image and get the optimal closed-form solution via the soft thresholding operation.Extensive experiments on one synthetic and three realistic datasets substantiate the effectiveness of our proposed method both quantitatively and qualitatively.In summary,we investigate in-depth to fully exploit the spatial and spectral correlation information for image denoising by utilizing statistical analysis and tensor decomposition.We develop four new and effective image denoising methods based on statistical analysis and tensor decomposition.The research outputs not only enrich the understanding of tensor based image modeling,but also demonstrate effective image denoising performance.