On The Synergy Between Nonconvex Extensions of The Tensor Nuclear Norm for Tensor Recovery

Abstract (excerpt)

Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank--e.g. the CP rank and the Tucker rank. Many low-rank tensor recovery methods are focused on the Tucker rank. Since the Tucker rank is nonconvex and discontinuous, many relaxations of the Tucker rank have been proposed, e.g., the tensor nuclear norm, weighted tensor nuclear norm, and weighted tensor Schatten-$p$ norm. In particular, the weighted tensor Schatten-p norm has two parameters, the weight and $p$, and the tensor nuclear norm and

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