Improved Robust Low-Rank Regularization Tensor Completion

With the rapid development of modern information technologies such as multimedia and artificial intelligence,more and more multi-dimensional data with complicated structures and large scale has emerged in the fields of computer vision and signal processing.However,tensor data could be corrupted,such as noisy corruption,missing values,during the acquisition and transmission process due to the limitations of imaging equipments,imaging environments,and transmission conditions.Using the low-rank characteristics of multimedia tensors,multi-dimensional tensor data can be recovered from the original data,and it has been widely studied by scholars in the field of machine learning.Taking the third-order tensor singular value decomposition algebraic framework as the carrier,the traditional Tensor Nuclear Norm(TNN)regularization low-rank completion model is equally treated singular value.It limits the flexibility of the constructed model.When the unknown elements of the original tensor data are much larger than the known elements,the instability of the solution based on the TNN regularization model is caused.Aiming at the above issues,a mixed norm composed of the weighted nuclear norm and the weighted Frobenius norm regularized tensor completion model is proposed.The model adaptively assigns weights to different singular values and works out the prior knowledge of singular values ignored by the traditional regularization.The model sets smaller weights to larger singular values and larger weights to smaller singular values.Based on the non-descending order of weights,the theoretical forms of the weighted nuclear norm and the weighted Frobenius norm proximal operator are studied.It is proved that without iterative threshold and weight calculation,the optimal closed-form solution is directly calculated based on the relationship between the singular value of the observed tensor and the regularization parameter.Finally,the experimental results of synthetic data and real data show that compared with the existing low-rank completion model,the original tensor data can be recovered with more stable and higher accuracy.