Identifiability of Kronecker-structured Dictionaries for Tensor Data

12/10/2017

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by   Zahra Shakeri, et al.

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This paper derives sufficient conditions for reliable recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing Kth-order tensor data. Tensor observations are generated by a Kronecker-structured dictionary and sparse coefficient tensors that follow the separable sparsity model. This work provides sufficient conditions on the underlying coordinate dictionaries, coefficient and noise distributions, and number of samples that guarantee recovery of the individual coordinate dictionaries up to a specified error with high probability. In particular, the sample complexity to recover K coordinate dictionaries with dimensions m_k× p_k up to estimation error r_k is shown to be _k ∈ [K]O(m_kp_k^3r_k^-2).