DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds

TL;DR

DECONET is a deep unfolding network designed for analysis-based compressed sensing that jointly learns a decoder and sparsifying operator, with theoretical generalization bounds and superior empirical performance on synthetic and real data.

Contribution

The paper introduces DECONET, a novel unfolding network with theoretical generalization error bounds for analysis-sparsity-based compressed sensing.

Findings

DECONET outperforms state-of-the-art unfolding networks on various datasets.

Theoretical bounds on generalization error are validated experimentally.

DECONET effectively reconstructs signals from noisy, incomplete measurements.

Abstract

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.