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.

翻译：解折叠网络在压缩感知领域展现出了良好的应用前景，然而其泛化能力的探究仍处于起步阶段。本文针对一种基于ADMM的最先进解折叠网络进行泛化分析，该网络联合学习压缩感知解码器与稀疏化冗余分析算子。为此，我们首先对可学习的稀疏化器施加结构约束，该约束参数化网络的假设空间；随后估计该假设空间的Rademacher复杂度；基于此估计值，推导出所研究网络的泛化误差界。最后，通过合成数据集与真实数据集验证理论有效性，并与当前最先进的解折叠网络进行数值对比。实验结果表明，本文提出的框架符合理论发现，并在所有数据集上持续优于基线方法。