  This paper derives sufficient conditions for local recovery of coordinate
dictionaries comprising a Kronecker-structured dictionary that is used for
representing $K$th-order tensor data. Tensor observations are assumed to be
generated from a Kronecker-structured dictionary multiplied by 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, as
a local minimum of the objective function, with high probability. In
particular, the sample complexity to recover $K$ coordinate dictionaries with
dimensions $m_k \times p_k$ up to estimation error $\varepsilon_k$ is shown to
be $\max_{k \in [K]}\mathcal{O}(m_kp_k^3\varepsilon_k^{-2})$.
