# Robust lEarned Shrinkage-Thresholding (REST): Robust unrolling for sparse recover

arXiv: https://arxiv.org/abs/2110.10391 · HTML: https://mlsanity.com/paper/2110.10391/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 48 references that are in the map.
- First posted on arXiv 20 Oct 2021.

## Builds on (most cited first, 13 of 13)

- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Deep Learning with Differential Privacy](https://mlsanity.com/paper/1607.00133/) (2016)
- [Image Super-Resolution Using Deep Convolutional Networks](https://mlsanity.com/paper/1501.00092/) (2014)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Defense-GAN: Protecting Classifiers Against Adversarial Attacks Using Generative Models](https://mlsanity.com/paper/1805.06605/) (2018)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Towards Deep Neural Network Architectures Robust to Adversarial Examples](https://mlsanity.com/paper/1412.5068/) (2014)
- [Enhancing Robustness of Machine Learning Systems via Data Transformations](https://mlsanity.com/paper/1704.02654/) (2017)
- [Learned SPARCOM: Unfolded Deep Super-Resolution Microscopy](https://mlsanity.com/paper/2004.09270/) (2020)
- [Multimodal Image Super-resolution via Joint Sparse Representations induced by Coupled Dictionaries](https://mlsanity.com/paper/1709.08680/) (2017)
- [When to Use Convolutional Neural Networks for Inverse Problems](https://mlsanity.com/paper/2003.13820/) (2020)

## Built on by (most cited first, 1 of 1)

- [A Bayesian Based Deep Unrolling Algorithm for Single-Photon Lidar Systems](https://mlsanity.com/paper/2201.10910/) (2022)

## Abstract (arXiv)

In this paper, we consider deep neural networks for solving inverse problems that are robust to forward model mis-specifications. Specifically, we treat sensing problems with model mismatch where one wishes to recover a sparse high-dimensional vector from low-dimensional observations subject to uncertainty in the measurement operator. We then design a new robust deep neural network architecture by applying algorithm unfolding techniques to a robust version of the underlying recovery problem. Our proposed network - named Robust lEarned Shrinkage-Thresholding (REST) - exhibits an additional normalization processing compared to Learned Iterative Shrinkage-Thresholding Algorithm (LISTA), leading to reliable recovery of the signal under sample-wise varying model mismatch. The proposed REST network is shown to outperform state-of-the-art model-based and data-driven algorithms in both compressive sensing and radar imaging problems wherein model mismatch is taken into consideration.