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Guarantees of Augmented Trace Norm Models in Tensor Recovery

2019-11-11 | |  60 |   58 |   0
Abstract This paper studies the recovery guarantees of the models of minimizing X ? + 2? 1 X 2F where X is a tensor and X ? and X F are the trace and Frobenius norm of respectively. We show that they can ef?ciently 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 , 1 minimizing X ? + 2? X 2F returns the same solution as minimizing X ? almost whenever ? ? 0 10 max X(i) 2 . i

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