Research And Application Of Missing Data Completion Model Based On Tensor Ring Nuclear Norm

The rapid development of sensor technology enables people to obtain large-scale,multidi-mensional data in computer vision,neuroscience,signal processing and other fields.However,due to the objective factors such as equipment failure,network delay,external objects cover and so on,the acquired data is usually incomplete(only part of the elements can be seen),and the traditional equipment and algorithms are often unable to effectively process incom-plete data.Therefore,more and more researchers pay attention to how to use only partial data to recover the complete tensor.In addition,the data is usually mixed with Gaussian noise or salt and pepper noise in the process of data collection.It is of great significance and value to overcome the interference of missing and noise and realize the effective recovery of data.Tensor low-rank representation learning is widely used in machine learning,pattern recog-nition,signal processing and other fields because of the low-rank structure of high-order data.In recent years,low-rank tensor ring models can effectively mine high-order data structures,which can solve the problem of tensor completion more effectively than other tensor decompo-sition models.Therefore,based on the tensor ring decomposition model,this thesis studies the incomplete tensor completion problem and tensor denoising completion problem respectively.The specific research work is as follows:In order to describe the low rank of tensor data more accurately,we propose a weighted tensor ring nuclear norm.Compared with the tensor ring nuclear norm in the previous study,weighted tensor ring nuclear norm proposed in this thesis weight the singular values so that the larger singular values are only punished less,and the smaller singular values are punished more,so as to achieve more accurate low-rank modeling.Based on the proposed nuclear norm of weighted tensor rings,a low-rank tensor ring completion model and an incomplete ten-sor completion model contaminated by Gaussian noise are established.In order to solve the proposed model effectively,the alternate direction multiplier method is used to update and optimize the model.Through experiments on a large number of real data,the superiority of the proposed model in tensor completion task and tensor denoising task is demonstrated.In this thesis,the incomplete tensor completion problem of salt and pepper noise pollu-tion is considered.In low-rank modeling,we propose a truncated tensor ring nuclear norm to avoid noise by penalizing smaller singular values.Specifically,by intercepting the first r singular values of the tensor ring cyclic unfolding matrix,it is guaranteed to be unpunished when updating,and only the remaining singular values are minimized.In noise modeling,the₁norm is used to describe the sparsity of salt-and-pepper noise in data.A low-rank tensor ring denoising completion model based on minimizing truncated tensor ring nuclear norm is proposed.At the same time,the alternate direction multiplier method is proposed to update and optimize the model.Experiments show that our model achieves high data completion effect in both simulation data and visual data.