  Inspired by the recent success of deep neural networks and the recent efforts
to develop multi-layer dictionary models, we propose a Deep Analysis dictionary
Model (DeepAM) which is optimized to address a specific regression task known
as single image super-resolution. Contrary to other multi-layer dictionary
models, our architecture contains L layers of analysis dictionary and
soft-thresholding operators to gradually extract high-level features and a
layer of synthesis dictionary which is designed to optimize the regression task
at hand. In our approach, each analysis dictionary is partitioned into two
sub-dictionaries: an Information Preserving Analysis Dictionary (IPAD) and a
Clustering Analysis Dictionary (CAD). The IPAD together with the corresponding
soft-thresholds is designed to pass the key information from the previous layer
to the next layer, while the CAD together with the corresponding
soft-thresholding operator is designed to produce a sparse feature
representation of its input data that facilitates discrimination of key
features. DeepAM uses both supervised and unsupervised setup. Simulation
results show that the proposed deep analysis dictionary model achieves better
performance compared to a deep neural network that has the same structure and
is optimized using back-propagation when training datasets are small.
