Abstract

This paper studies the recovery guarantees of the models of minimizing ||X|| ∗ + 1/2a ||X|| 2 F where X is a tensor and ||X|| ∗ and ||X|| F are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing ||X|| ∗ under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor X 0 , minimizing ||X|| ∗ + 1/2a ||X|| 2 F returns the same solution as minimizing ||X|| ∗ almost whenever α ≥ 10max ||X 0 (i) || 2 .

Guarantees of Augmented Trace Norm Models in Tensor Recovery / 1670 Ziqiang Shi, Jiqing Han, Tieran Zheng, Ji Li This paper studies the recovery guarantees of the models of minimizing ||X|| ∗ + 1/2a ||X|| 2 F where X is a tensor and ||X|| ∗ and ||X|| F are the trace and Frobenius norm of respectively. We show that they can efficiently recover low-rank tensors. In particular, they enjoy exact guarantees similar to those known for minimizing ||X|| ∗ under the conditions on the sensing operator such as its null-space property, restricted isometry property, or spherical section property. To recover a low-rank tensor X 0 , minimizing ||X|| ∗ + 1/2a ||X|| 2 F returns the same solution as minimizing ||X|| ∗ almost whenever α ≥ 10max ||X 0 (i) || 2 .