A Research Of High-dimensional Data Recovery Model And Algorithm Based On Tensor Ring Decomposition With Factors Regularization

With the rapid development of technology,the acquired data in the real world is emerging with higher dimensions(i.e.high-dimensional data)and more complex structural information.However,in the data acquisition process,acquired tensor data often suffer from missing entries,which severely damage the data quality and hinder subsequent applications.High-dimensional data recovery aims at estimating missing values from partial observations to improve data quality and can be mathematically modeled as tensor completion problem.Tensor completion is an ill-posed problem,and thus we need to introduce prior knowledge by a regularization term to address this problem.Highdimensional data acquired in the real world often have strong redundancy,which is mathematically expressed as low-rankness.The low-rank constraint is a powerful tool to exploit the inner relationship of high-dimensional data.Tensor ring(TR)decomposition approximates a high-order tensor using the circularly multilinear products of a sequence of third-order core tensors,which may be favorable for capturing the global low-rankness of high-dimensional data.Recently,TR decomposition has been increasingly applied to the high-dimensional data recovery problem and obtained impressive performance.However,the understanding of the physical interpretation of TR factors is not clear.1.In this thesis,we first empirically discover the physical interpretation of TR factors in the gradient domain(termed as gradient factors)and then give the theoretical justification.Based on the interpretable gradient factors,we suggest a TR decomposition-based model with interpretable gradient factors regularization(TR-GFR)for high-dimensional data recovery.More concretely,we consider the low-rankness and transformed sparsity priors of gradient factors to boost the performance and robustness of TR decompositionbased model.2.This thesis develops an efficient proximal alternating minimization algorithm to solve the proposed model and theoretically establish the convergence guarantee.Numerical experiments on multispectral images,hyperspectral images,color videos,and traffic data validate that the proposed TR-GFR is superior to the compared state-of-the-art methods in terms of evaluation metrics and more robust with TR rank.