Abstract
This work addresses the problem of structured dictionary learning for computing sparse representations of tensor-structured data. It introduces a low-separation-rank dictionary learning (LSR-DL) model that better captures the structure of tensor data by generalizing the separable dictionary learning model. A dictionary with p columns that is generated from the LSR-DL model is shown to be locally identifiable from noisy observations with recovery error at most ρ given that the number of training samples scales with (# of degrees of freedom in the dictionary)×p 2 ρ −2 .