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

arXiv: https://arxiv.org/abs/2205.07050 · HTML: https://mlsanity.com/paper/2205.07050/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 70 references that are in the map.
- First posted on arXiv 14 May 2022.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Information-theoretic analysis of generalization capability of learning algorithms](https://mlsanity.com/paper/1705.07809/) (2017)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Chaining Mutual Information and Tightening Generalization Bounds](https://mlsanity.com/paper/1806.03803/) (2018)
- [Collapse of Deep and Narrow Neural Nets](https://mlsanity.com/paper/1808.04947/) (2018)
- [DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing](https://mlsanity.com/paper/1702.05743/) (2017)
- [Deep Unfolding of a Proximal Interior Point Method for Image Restoration](https://mlsanity.com/paper/1812.04276/) (2018)
- [Compressive Sensing and Neural Networks from a Statistical Learning Perspective](https://mlsanity.com/paper/2010.15658/) (2020)
- [Generalization Error Bounds for Iterative Recovery Algorithms Unfolded as Neural Networks](https://mlsanity.com/paper/2112.04364/) (2021)
- [ADMM-DAD net: a deep unfolding network for analysis compressed sensing](https://mlsanity.com/paper/2110.06986/) (2021)
- [Dictionary Learning for Blind One Bit Compressed Sensing](https://mlsanity.com/paper/1508.07648/) (2015)
- [Interpretable Deep Recurrent Neural Networks via Unfolding Reweighted ℓ1-ℓ1 Minimization: Architecture Design and Generalization Analysis](https://mlsanity.com/paper/2003.08334/) (2020)
- [A Robust Deep Unfolded Network for Sparse Signal Recovery from Noisy Binary Measurements](https://mlsanity.com/paper/2010.07564/) (2020)

## Built on by (most cited first, 4 of 4)

- [Generalization analysis of an unfolding network for analysis-based Compressed Sensing](https://mlsanity.com/paper/2303.05582/) (2023)
- [On Generalization Bounds for Deep Compound Gaussian Neural Networks](https://mlsanity.com/paper/2402.13106/) (2024)
- [How to warm-start your unfolding network](https://mlsanity.com/paper/2502.01854/) (2025)
- [Adversarial generalization of unfolding (model-based) networks](https://mlsanity.com/paper/2509.15370/) (2025)

## Abstract (arXiv)

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.