  Sparsity driven signal processing has gained tremendous popularity in the
last decade. At its core, the assumption is that the signal of interest is
sparse with respect to either a fixed transformation or a signal dependent
dictionary. To better capture the data characteristics, various dictionary
learning methods have been proposed for both reconstruction and classification
tasks. For classification particularly, most approaches proposed so far have
focused on designing explicit constraints on the sparse code to improve
classification accuracy while simply adopting $l_0$-norm or $l_1$-norm for
sparsity regularization. Motivated by the success of structured sparsity in the
area of Compressed Sensing, we propose a structured dictionary learning
framework (StructDL) that incorporates the structure information on both group
and task levels in the learning process. Its benefits are two-fold: (i) the
label consistency between dictionary atoms and training data are implicitly
enforced; and (ii) the classification performance is more robust in the cases
of a small dictionary size or limited training data than other techniques.
Using the subspace model, we derive the conditions for StructDL to guarantee
the performance and show theoretically that StructDL is superior to $l_0$-norm
or $l_1$-norm regularized dictionary learning for classification. Extensive
experiments have been performed on both synthetic simulations and real world
applications, such as face recognition and object classification, to
demonstrate the validity of the proposed DL framework.
