  On account of its many successes in inference tasks and denoising
applications, Dictionary Learning (DL) and its related sparse optimization
problems have garnered a lot of research interest. While most solutions have
focused on single layer dictionaries, the improved recently proposed Deep DL
(DDL) methods have also fallen short on a number of issues. We propose herein,
a novel DDL approach where each DL layer can be formulated as a combination of
one linear layer and a Recurrent Neural Network (RNN). The RNN is shown to
flexibly account for the layer-associated and learned metric. Our proposed work
unveils new insights into Neural Networks and DDL and provides a new, efficient
and competitive approach to jointly learn a deep transform and a metric for
inference applications. Extensive experiments are carried out to demonstrate
that the proposed method can not only outperform existing DDL but also
state-of-the-art generic CNNs.
