A Low Rank Approximation For High Order Image Based On Generalized Matrix Model

Low rank approximation is an important part of image processing,transmission and recognition.Image is an important medium for people to obtain external information.Most of the images in nature are second-order gray-scale images or third-order RGB images,and the images are easily interfered by various external factors in the transmission process,which will challenge the image low rank approximation,resulting in the problems of low peak signal-to-noise ratio of existing algorithms,poor reconstruction effect,etc.,which are difficult to adapt to the needs of big data development.In recent years,singular value decomposition,high-order singular value decomposition and high-order orthogonal iteration have been widely used in image low rank approximation and achieved good results.However,in view of the high-order information of the image and the mutual restriction between pixels,the classical low rank approximation algorithm can not make good use of the spatial structure and high-order information of the image.In this paper,the high-order image low rank approximation method based on the generalized matrix model is studied in depth.The specific research results are given as follows:(1)In order to solve the problem that the traditional SVD low rank approximation is not ideal,A low rank approximation algorithm for high-order image based on Tensorial singular value decomposition(TSVD)is proposed and improved,At the same time,it is applied to image denoising.Firstly,for the original two-dimensional gray-scale image,the generalized high-order image is obtained by using the generalized matrix model,the traditional singular value decomposition is solved by slicing operation in the Fourier domain,and then the approximate generalized matrix is obtained by inverse Fourier transform;Secondly,Gaussian noise is added to the original two-dimensional gray-scale image,and the neighborhood ofthe noisy image is selected by using the generalized matrix model to get the high-order noisy image,and the generalized singular value decomposition and eigenvalue selection are done for it;Finally,the performance of low rank approximation is analyzed by peak SNR and average structure similarity.(2)A low rank approximation method for high-order images based on generalized high-order singular value decomposition is proposed.First of all,the implementation steps of high-order SVD(HOSVD)algorithm are introduced;then the traditional algorithm is improved,and the traditional matrix in different modes is expanded by using generalized matrix model,so that the original matrix is transformed into generalized matrix;then the generalized singular value decomposition is carried out by using Fourier transform to get the generalized left singular matrix in different modes;finally,the anti Fourier transform is used to get the generalized left singular matrix in different modes The Approximate Generalized tensor is obtained by leaf transform,and the optimal approximation effect is obtained by peak signal-to-noise ratio.(3)Low rank approximation algorithm based on high order orthogonal iteration of generalized tensor is proposed.First,generalized high-order singular value decomposition is obtained by generalized matrix model generalization;second,generalized left singular matrix of mode n is obtained by generalized high-order singular value decomposition,which is combined according to the formula,and then generalized left singular matrix of new mode n is obtained by mode n expansion;then the eigenvalues of the new generalized left singular matrix of mode n are selected;finally,near Generalized core tensor and generalized approximate tensor after similitude.Finally,the simulation results show that the generalized matrix algorithm proposed in this paper is obviously better than the traditional matrix algorithm,and with the expansion of the generalized matrix order,the image approximation effect and denoising effect are significantly improved...