Recovery of Corrupted Low-Rank Tensors

Abstract

This paper studies the problem of recovering low-rank tensors, and the tensors are corrupted by both impulse and Gaussian noise. The problem is well accomplished by integrating the tensor nuclear norm and the l 1 -norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l 1 -norm is used to exploit the impulse noise.Then, this optimization problem is solved by some augmented-Lagrangianbased algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.