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

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.

Accepted in IEEE Transactions on Signal Processing

References in corpus (4)

• ADMM-DAD net: a deep unfolding network for analysis compressed sensing
• Spark Deficient Gabor Frame Provides a Novel Analysis Operator for Compressed Sensing
• Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks
• Generalization Bounds for Stochastic Gradient Descent via Localized $\epsilon$-Covers

Cited by in corpus (1)

• Generalization analysis of an unfolding network for analysis-based Compressed Sensing