  Unfolding networks have shown promising results in the Compressed Sensing
(CS) field. Yet, the investigation of their generalization ability is still in
its infancy. In this paper, we perform generalization analysis of a
state-of-the-art ADMM-based unfolding network, which jointly learns a decoder
for CS and a sparsifying redundant analysis operator. To this end, we first
impose a structural constraint on the learnable sparsifier, which parametrizes
the network's hypothesis class. For the latter, we estimate its Rademacher
complexity. With this estimate in hand, we deliver generalization error bounds
for the examined network. Finally, the validity of our theory is assessed and
numerical comparisons to a state-of-the-art unfolding network are made, on
synthetic and real-world datasets. Our experimental results demonstrate that
our proposed framework complies with our theoretical findings and outperforms
the baseline, consistently for all datasets.
