  This work addresses the problem of learning sparse representations of tensor
data using structured dictionary learning. It proposes learning a mixture of
separable dictionaries to better capture the structure of tensor data by
generalizing the separable dictionary learning model. Two different approaches
for learning mixture of separable dictionaries are explored and sufficient
conditions for local identifiability of the underlying dictionary are derived
in each case. Moreover, computational algorithms are developed to solve the
problem of learning mixture of separable dictionaries in both batch and online
settings. Numerical experiments are used to show the usefulness of the proposed
model and the efficacy of the developed algorithms.
