Tensor Robust Principal Component Analysis with A New Tensor Nuclear Norm

Understand

In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum.

• Our model is based on the recently proposed tensor-tensor product (or t-product).
• Induced by the t-product, we first rigorously deduce the tensor spectral norm, tensor nuclear norm, and tensor average rank, and show that the tensor nuclear norm is the convex envelope of the tensor average rank within the unit ball of the tensor spectral norm.
• These definitions, their relationships and properties are consistent with matrix cases.