Guarantees of Augmented Trace Norm Models in Tensor Recovery

07/23/2012

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by   Ziqiang Shi, et al.

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This paper studies the recovery guarantees of the models of minimizing X_*+1/2αX_F^2 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_*+1/2αX_F^2 returns the same solution as minimizing X_* almost whenever α≥10_iX^0_(i)_2.