We present a new deep unfolding network for analysis-sparsity-based Compressed Sensing. The proposed network coined Decoding Network (DECONET) jointly learns a decoder that reconstructs vectors from their incomplete, noisy measurements and a redundant sparsifying analysis operator, which is shared across the layers of DECONET. Moreover, we formulate the hypothesis class of DECONET and estimate its associated Rademacher complexity. Then, we use this estimate to deliver meaningful upper bounds for the generalization error of DECONET. Finally, the validity of our theoretical results is assessed and comparisons to state-of-the-art unfolding networks are made, on both synthetic and real-world datasets. Experimental results indicate that our proposed network outperforms the baselines, consistently for all datasets, and its behaviour complies with our theoretical findings.

翻译：我们提出了一种新的深度展开网络，用于基于分析稀疏性的压缩感知。该网络被称为解码网络（DECONET），它联合学习一个解码器（用于从不完整、带噪声的测量中重建向量）和一个冗余的稀疏化分析算子，该算子在各网络层间共享。此外，我们构建了DECONET的假设类，并估计了其相关的Rademacher复杂度。随后，利用该估计结果给出了DECONET泛化误差的有效上界。最后，我们在合成数据集和真实数据集上评估了理论结果的有效性，并与现有最先进的展开网络进行了比较。实验结果表明，我们提出的网络在所有数据集上均优于基线方法，且其行为与我们的理论发现一致。