Information Theoretic Bounds for Tensor Rank Minimization over Finite Fields

@article{Emad2011InformationTB,
  title={Information Theoretic Bounds for Tensor Rank Minimization over Finite Fields},
  author={Amin Emad and Olgica Milenkovic},
  journal={2011 IEEE Global Telecommunications Conference - GLOBECOM 2011},
  year={2011},
  pages={1-5}
}
We consider the problem of noiseless and noisy low- rank tensor completion from a set of random linear measurements. In our derivations, we assume that the entries of the tensor belong to a finite field of arbitrary size and that reconstruction is based on a rank minimization framework. The derived results show that the smallest number of measurements needed for exact reconstruction is upper bounded by the product of the rank, the order, and the dimension of a cubic tensor. Furthermore, this… CONTINUE READING

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