On the Synergy between Nonconvex Extensions of the Tensor Nuclear Norm for Tensor Recovery

Low-rank tensor recovery has attracted much attention among various approaches. A rank several definitions, unlike the matrix rank—e.g., CP and Tucker rank. Many low-rank methods are focused on Since is nonconvex discontinuous, many relaxations of have been proposed, e.g., sum nuclear norm, weighted schatten-p norm. In particular, norm two parameters, weight p, special cases these parameters. However, there no detailed discussion whether effects weighting p synergistic. this paper, we propose a novel completion model using to reveal relationships between p. To clarify complex such as necessary, compare them with simple method rank-constrained minimization. It was found that did not outperform unless original could be accurately known. If can obtain ideal weight, p=1 sufficient, although it necessary set p<1 when weights obtained from observations. These results consistent existing reports.