Adaptive Robustness Matrix And Tensor Completion Methods

With the progress of society and the rapid development of information science,there are many large-scale feature data in many practical applications of science and engineering.These data may have problems such as missing,damaged,and distorted data.This is due to the fact that the data in the process of storage or transport inevitably affected by noise pollution or other factors.These problems will seriously affect the accuracy of data analysis.In order to solve this type of problem,data completion technology came into being.Moreover,data completion technology plays a very important role in data analysis and processing.It has been widely used in the fields of image restoration,computer vision,recommendation systems and video restoration.Data completion refers to the use of some prior information and observation data to recover unknown missing data.In general,data completion algorithms include matrix completion algorithms and tensor completion algorithms.There are many mature and efficient matrix and tensor completion algorithms.However,in practical applications,for missing matrices damaged by outlier,the traditional matrix completion unconstrained optimization model is sensitive to outliers,so the robustness is poor.In order to improve the recovery situation,the main work of this paper is as follows:1.In the traditional unconstrained optimization model of matrix completion,the square Fnorm is used as the loss term to recover the missing values in the matrix.However,the square F-norm is sensitive to outliers,the robustness for recovering the missing matrix damaged by outlier is not ideal.In order to solve this problem,an adaptive robust matrix completion method is proposed.In this method,truncated kernel norm is used as the low-rank approximation of the rank function in the objective function,and the F-norm of outlier robustness is used as the loss term to recover the missing values in the matrix,which reduces the influence of outliers on the algorithm and improves the recovery accuracy.In order to solve this model,a dynamic weight parameter is introduced by convex optimization technique,which can be used to adjust the next iteration adaptively according to the magnitude of the recovery error when updating the recovery value,and then an effective iteration method is established to solve the optimization problem.Numerical experiments show that the algorithm is robust and accurate when dealing with data destroyed by outlier.2.The low-rank matrix completion method processes the input data in a two-dimensional manner.Specifically,when recovering color images,the algorithm is applied to each channel separately,and then the results are simply combined.It has an obvious flaw,that is,it does not consider the structural information between channels.Although vectors and matrices are easier to handle,converting multidimensional tensors into matrices or vectors often results in loss of information and performance degradation.One of the effective ways of tensor data processing is to make full use of the multi-dimensional structure of the rich information contained in tensor data.Therefore,considering the structural information of the data,color images and videos are taken as three-dimensional data,and the improved completion model is extended from the matrix case to the tensor case.It is described as an adaptive robust tensor completion method.Experiments show that the proposed method can achieve better recovery effect.