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

arXiv: https://arxiv.org/abs/2303.05582 · HTML: https://mlsanity.com/paper/2303.05582/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 63 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 20 of 20)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Stronger generalization bounds for deep nets via a compression approach](https://mlsanity.com/paper/1802.05296/) (2018)
- [Generalization Bounds of Stochastic Gradient Descent for Wide and Deep Neural Networks](https://mlsanity.com/paper/1905.13210/) (2019)
- [A vector-contraction inequality for Rademacher complexities](https://mlsanity.com/paper/1605.00251/) (2016)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Deep Unfolding: Model-Based Inspiration of Novel Deep Architectures](https://mlsanity.com/paper/1409.2574/) (2014)
- [Iterative Algorithm Induced Deep-Unfolding Neural Networks: Precoding Design for Multiuser MIMO Systems](https://mlsanity.com/paper/2006.08099/) (2020)
- [Information-Theoretic Lower Bounds for Compressive Sensing with Generative Models](https://mlsanity.com/paper/1908.10744/) (2019)
- [Memory-augmented Deep Unfolding Network for Guided Image Super-resolution](https://mlsanity.com/paper/2203.04960/) (2022)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Compressive Sensing and Neural Networks from a Statistical Learning Perspective](https://mlsanity.com/paper/2010.15658/) (2020)
- [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)
- [Fast Compressive Sensing Recovery Using Generative Models with Structured Latent Variables](https://mlsanity.com/paper/1902.06913/) (2019)
- [LADMM-Net: An Unrolled Deep Network For Spectral Image Fusion From Compressive Data](https://mlsanity.com/paper/2103.00940/) (2021)
- [DECONET: an Unfolding Network for Analysis-based Compressed Sensing with Generalization Error Bounds](https://mlsanity.com/paper/2205.07050/) (2022)
- [Interpretable Deep Recurrent Neural Networks via Unfolding Reweighted ℓ1-ℓ1 Minimization: Architecture Design and Generalization Analysis](https://mlsanity.com/paper/2003.08334/) (2020)

## Built on by (most cited first, 2 of 2)

- [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)

Unfolding networks have shown promising results in the Compressed Sensing (CS) field. Yet, the investigation of their generalization ability is still in its infancy. In this paper, we perform a generalization analysis of a state-of-the-art ADMM-based unfolding network, which jointly learns a decoder for CS and a sparsifying redundant analysis operator. To this end, we first impose a structural constraint on the learnable sparsifier, which parametrizes the network's hypothesis class. For the latter, we estimate its Rademacher complexity. With this estimate in hand, we deliver generalization error bounds -- which scale like the square root of the number of layers -- for the examined network. Finally, the validity of our theory is assessed and numerical comparisons to a state-of-the-art unfolding network are made, on synthetic and real-world datasets. Our experimental results demonstrate that our proposed framework complies with our theoretical findings and outperforms the baseline, consistently for all datasets.