  Based on its great successes in inference and denosing tasks, Dictionary
Learning (DL) and its related sparse optimization formulations have garnered a
lot of research interest. While most solutions have focused on single layer
dictionaries, the recently improved Deep DL methods have also fallen short on a
number of issues. We hence propose a novel Deep DL approach where each DL layer
can be formulated and solved as a combination of one linear layer and a
Recurrent Neural Network, where the RNN is flexibly regraded as a
layer-associated learned metric. Our proposed work unveils new insights between
the Neural Networks and Deep DL, and provides a novel, efficient and
competitive approach to jointly learn the deep transforms and metrics.
Extensive experiments are carried out to demonstrate that the proposed method
can not only outperform existing Deep DL, but also state-of-the-art generic
Convolutional Neural Networks.
