DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds
This work addresses compressed sensing for signal processing applications, offering improved reconstruction with theoretical guarantees, but it is incremental as it builds on existing unfolding network frameworks.
The paper tackles the problem of reconstructing vectors from incomplete, noisy measurements in compressed sensing by proposing DECONET, a deep unfolding network that jointly learns a decoder and a sparsifying analysis operator, and it outperforms state-of-the-art baselines across all tested datasets.
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.