Matrix analysis
A Multilinear Singular Value Decomposition
SIAM Journal on Matrix Analysis and Applications
Tensor Decompositions and Applications
SIAM Review
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
Uncertainty principles and ideal atomic decomposition
IEEE Transactions on Information Theory
Sparse representations in unions of bases
IEEE Transactions on Information Theory
Decoding by linear programming
IEEE Transactions on Information Theory
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This paper studies the recovery guarantees of the models of minimizing ||χ||* + 1/2α||χ||F2 where χ is a tensor and ||χ||* and ||χ||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 ||χ||* 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 χ0, minimizing ||χ||* + 1/2α||χ||F2 returns the same solution as minimizing ||χ||* almost whenever α ≥ 10 max i ||X(i)0||2.