Research On Image Method Based On Low-Rank Tensor Decomposition

With the popularization and development of Internet and computer technology,image data is affected by many factors in the process of storage and transmission,which makes us unable to obtain complete and accurate information.Tensor decomposition has attracted wide attention in solving such problems.Since the image information tensor is known to be low-rank or approximately low-rank,the problem is usually transformed into a rank minimization problem to be solved.Aiming at the problems of data missing and noise in image data,based on tensor decomposition and the image to be inpainted as the research object,this paper studies the relevant theoretical methods in tensor completion problem,and mainly carries out two aspects of research work,the specific content is as follows:(1)Aiming at the problem that low-rank tensor singular value decomposition overuses different sparse constraints and underutilizes the potential structural relationship of data,which leads to high computational cost in image data processing and affects the quality of image inpainting,an image inpainting algorithm TNN-LTKM based on truncated nuclear norm and low-rank tensor kernel matrix was proposed.Firstly,the tensor truncated nuclear norm was introduced to accurately approximate the rank function to enhance the robustness of the optimization model.Secondly,the tensor nuclear norm in t-SVD was extended by increasing the kernel matrix nuclear norm,and a new potential nuclear norm containing the rank of the tensor tube and the rank of the kernel matrix was constructed to fully extract the low-rank structure in the kernel tensor and eliminate redundancy.Then,the augmented Lagrange alternating direction method of multipliers was used to optimize the above model.Finally,the experiments were carried out on three datasets of ZJU,Berkeley and Kodak Lossless,and the four evaluation indicators of relative square error,peak signalto-noise ratio,structural similarity and CPU running time were used to compare with the existing six algorithms.Experiments show that TNN-LTKM algorithm has good performance at low sampling rate.(2)Aiming at the problems that the existing algorithms have isometric contraction and the multiplication of tensor rank factors is not permutation invariant in the process of optimizing tensor nuclear norm,this paper proposed a robust low-rank tensor ring completion algorithm for latent matrix factorization under the framework of ring factorization tensor completion.Firstly,the tensor cycle unrolling operation is introduced to establish the relationship between tensor cycle unrolling matrix and tensor cycle unrolling matrix.Each latent component is approximated by low-rank matrix factorization of tensor cycle unrolling matrix,and it is applied to the tensor completion model of tensor cycle unrolling.Secondly,the nuclear norm regularization is introduced into the tensor ring factor,and the singular value decomposition is used as the alternating direction multiplier iteration process of the latent tensor ring factor,so that the optimization step of SVD is performed on a smaller scale.The rank-optimal latent tensor ring factor and recovery tensor are obtained,and the computational cost of the SVD operation is reduced.Finally,the experimental results on Facade,DTD and Celeb A-HQ datasets show that the proposed algorithm has certain advantages in image restoration compared with the existing nine algorithms through four evaluation indicators.On the basis of the above research,an image inpainting prototype sy stem based on low-rank tensor decomposition is designed and developed,which can effectively verify the proposed method.