Visual Data Recovery Based On Tensor Completion

When people collect data,it is inevitable that data will be lost due to equipment interruption and equipment damage.In order to make full use of the effective information of data,the data completion problem has gradually become the focus of computer vision and machine learning.However,with the advent of high-dimensional data,the traditional compression sensing and matrix completion methods can not solve the information completion problem well.In recent years,the research method of low-rank tensor completion problem has shown its powerful effect.The application value and theoretical significance.Based on the knowledge of tensor theory,this paper starts from two aspects,and deeply studies the single tensor data(image,video)completion methods and multiple tensor completion methods.The main contents of the work are as follows:(1)A visual data completion model based on spatial regularization.In order to preserve the smoothness of visual data,we are based on a simple idea: adjacent elements have similar values.A new tensor spatial regularization is proposed and transformed into a mathematical expression.In the tensor completion task,based on the proposed tensor spatial regularization,two low rank single tensor completion models are proposed in this paper.The first model considers both global and local aspects.The global information is expressed by the low rank property.By using the non-convex LogDet function instead of the tensor nuclear norm,the tensor real rank is more approximated.The local information is expressed by the tensor spatial regularization,and the combination can achieve a better recovery effect.Although this model has improved in recovery effect,the time complexity is still not optimistic.Based on this limitation,this paper proposes a visual data completion model.Based on the tensor algebra idea.Converting the large-scale computational cost into a smaller-scale computational cost by using Tucker decomposition,which effectively reduces the computational time overhead based on the accuracy.The validity and reliability of the proposed model are verified by experimental design and analysis.(2)A multi-tensor visual data completion with spatial model based on Laplace map.In real life,it is inevitable that multiple dataset scenarios will be collected at the same time.The task of multiple datasets completion is beyond the scope of the single tensor completion method,and considers that the single tensor completion method has a bad performance with low sampling rate.In this paper,the problem of poor performance is in-depth research.The existing multi-tensor completion model fills each data set by a tensor shared factor matrix.This processing method can only be applied to isomorphic datasets.This paper proposes a heterogeneous datasets completion model,by constructing a Laplacian graph by expanding the matrix of each dataset in a common mode.So as to achieve the purpose of mining the potential similarity structure shared among multiple datasets,this model can not only achieve better recovery effect,but also it can converge to the global optimal solution.Experiments show the effectiveness of the model.