Author(s)

Haiyan Fan, Gangyao Kuang

Department of Electronic Science and Engineering, National University of Defense Technology, Changsha, China.

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 l₁-norm in a unified convex relaxation framework. The nuclear norm is adopted to explore the low-rank components and the l₁-norm is used to exploit the impulse noise. Then, this optimization problem is solved by some augmented-Lagrangian-based algorithms. Some preliminary numerical experiments verify that the proposed method can well recover the corrupted low-rank tensors.

Low-Rank Tensor, Tensor Recovery, Augmented Lagrangian Method, Impulsive Noise, Mixed Noise

Fan, H. and Kuang, G. (2017) Recovery of Corrupted Low-Rank Tensors. Applied Mathematics, 8, 229-244. doi: 10.4236/am.2017.82019.