| With the continuous improvement of science and technology,society is in the era of information explosion.However,data loss may occur when it is transmitted.Data completing and recovery is essential.As the increasing of the amount of data,the storing of information changes from array into tensor.Tensor recovery is an effective way to solve the problem.It is widely used in signal processing,data mining,pattern recognition,image processing,computer vision and so on.The basic way of tensor recovery is to achieve data recovery by using some known part and grasping it’s correlation characteristics.These data are stored in the tensor present low rank characteristics.So solving the problem of data recovery can be transformed into solving an optimization problem of tensor recovery.Through the research of tensor recovery,three algorithms and models are proposed from the perspective of data correlation and the location structure of data element storage distribution.Respectively,in terms of tensor ring decomposition,imprecise tensor recovery model and algorithm,tensor recovery model and algorithm embedded in Hankel structure and structural constraint model and algorithm.The main research results are as follows:Firstly,based on the imprecise tensor recovery model of tensor ring decomposition,it can be seen from the definition of tensor ring decomposition that the tensor ring decomposition is a trace operation for the product of tensor kernel factor lateral slice matrix.Therefore,when performing tensor recovery,mode-2 unfolding matrix of tensor kernel factors is used to replace mode-1 and mode-3 unfolding matrices,which can reduce the computational complexity of the algorithm and improve the computational efficiency of the proposed tensor recovery algorithm.Further,the Hankel-structured tensor is constructed by embedding the data with multidirectional delay embedding technology(MDT).Starting from the structural characteristics of the data,the tensor recovery is realized by generating Hankel kernel factors to approximate the tensor with Hankel-structured.The convergence of the algorithm is further analyzed,the feasibility of the new algorithm is proved.Finally,the experiments on real world images show that the new algorithm can effectively recover the missing data and improve the recovery accuracy.Secondly,a structure constraint model and its corresponding algorithm were introduced by the tensor ring decomposition,which from the position structure of data element storage distribution.The key is that any tensor can be mapped a corresponding coefficient tensor by a set of bases,and the tensor recovery can be transformed into the recovery of its corresponding coefficient tensor.The structural constraint model is constructed.For the coefficient tensor,the non-negative low-rank constraint is applied to ensure that each element in the tensor is in its adjacent convex hull and the sparse constraint is applied to ensure that each element in the tensor involves as few adjacent elements as possible.A structure constraint algorithm based on tensor ring decomposition is proposed.The convergence of the algorithm is further analyzed and the feasibility of the new algorithm is proved.Finally,experiments are carried out on real world images,and the results show that the new algorithm can effectively improve their recovery accuracy. |
