Identifiability of Kronecker-structured Dictionaries for Tensor Data

This paper derives sufficient conditions for reliable recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$th-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 $m_k\times p_k$ up to estimation error $r_k$ is shown to be $\max_{k \in [K]}\mathcal{O}(m_kp_k^3r_k^{-2})$.