Tensor recovery based on rank adaptive and non-convex methods

Abstract

The growing popularity of tensor singular value decomposition (T-SVD) in tensor recovery problems and the N-tubal rank can be applied to higher order tensors. However, this method faces new challenges as it does not fully use the rank prior information of tensors and lacks non-convex relaxation methods. Thus, this paper applies a new non-convex function, called Minimax Logarithmic Concave Penalty (MLCP), based on the N-tubal rank method. Two MLCP models based on N-tubal rank are introduced for solving low-rank tensor completion (LRTC) and tensor robust principal component analysis (TRPCA) problems, along with corresponding solving algorithms. The effectiveness and superiority of these models are demonstrated through experiments on real datasets.