Generalization analysis of an unfolding network for analysis-based Compressed Sensing
This work addresses the generalization ability of unfolding networks for Compressed Sensing, which is an incremental contribution to the field.
The paper tackles the lack of generalization analysis for unfolding networks in Compressed Sensing by deriving error bounds for an ADMM-based network that learns a decoder and sparsifying operator, showing it outperforms a baseline on synthetic and real-world datasets.
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 a 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 -- which scale like the square root of the number of layers -- 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.