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 X⁰, minimizing ||X||_∗ + 1/2a ||X||²_F returns the same solution as minimizing ||X||_∗ almost whenever α ≥ 10max ||X⁰_(i)||₂.