# Measuring Robustness in Deep Learning Based Compressive Sensing

arXiv: https://arxiv.org/abs/2102.06103 · HTML: https://mlsanity.com/paper/2102.06103/

## Key facts

- Cited by 53 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2021.

## Built on by (most cited first, 30 of 53)

- [Robust Compressed Sensing MRI with Deep Generative Priors](https://mlsanity.com/paper/2108.01368/) (2021)
- [Accuracy on the Line: On the Strong Correlation Between Out-of-Distribution and In-Distribution Generalization](https://mlsanity.com/paper/2107.04649/) (2021)
- [Monarch: Expressive Structured Matrices for Efficient and Accurate Training](https://mlsanity.com/paper/2204.00595/) (2022)
- [Zero-Shot Self-Supervised Learning for MRI Reconstruction](https://mlsanity.com/paper/2102.07737/) (2021)
- [DDM2: Self-Supervised Diffusion MRI Denoising with Generative Diffusion Models](https://mlsanity.com/paper/2302.03018/) (2023)
- [SKM-TEA: A Dataset for Accelerated MRI Reconstruction with Dense Image Labels for Quantitative Clinical Evaluation](https://mlsanity.com/paper/2203.06823/) (2022)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Data augmentation for deep learning based accelerated MRI reconstruction with limited data](https://mlsanity.com/paper/2106.14947/) (2021)
- [RS2G: Data-Driven Scene-Graph Extraction and Embedding for Robust Autonomous Perception and Scenario Understanding](https://mlsanity.com/paper/2304.08600/) (2023)
- [Steerable Conditional Diffusion for Out-of-Distribution Adaptation in Medical Image Reconstruction](https://mlsanity.com/paper/2308.14409/) (2023)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Near-Exact Recovery for Tomographic Inverse Problems via Deep Learning](https://mlsanity.com/paper/2206.07050/) (2022)
- [Score-Guided Intermediate Layer Optimization: Fast Langevin Mixing for Inverse Problems](https://mlsanity.com/paper/2206.09104/) (2022)
- [Adversarial Robustness of MR Image Reconstruction under Realistic Perturbations](https://mlsanity.com/paper/2208.03161/) (2022)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Robustness of Deep Learning for Accelerated MRI: Benefits of Diverse Training Data](https://mlsanity.com/paper/2312.10271/) (2023)
- [Deep Learning for Accelerated and Robust MRI Reconstruction: a Review](https://mlsanity.com/paper/2404.15692/) (2024)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)
- [To be or not to be stable, that is the question: understanding neural networks for inverse problems](https://mlsanity.com/paper/2211.13692/) (2022)
- [Learning Provably Robust Estimators for Inverse Problems via Jittering](https://mlsanity.com/paper/2307.12822/) (2023)
- [Optimal MRI Undersampling Patterns for Ultimate Benefit of Medical Vision Tasks](https://mlsanity.com/paper/2108.04914/) (2021)
- [Inverse Problems Leveraging Pre-trained Contrastive Representations](https://mlsanity.com/paper/2110.07439/) (2021)
- [Memory-efficient model-based deep learning with convergence and robustness guarantees](https://mlsanity.com/paper/2206.04797/) (2022)
- [Stability of Image-Reconstruction Algorithms](https://mlsanity.com/paper/2206.07128/) (2022)
- [On Logical Extrapolation for Mazes with Recurrent and Implicit Networks](https://mlsanity.com/paper/2410.03020/) (2024)
- [Self-Supervised Diffusion MRI Denoising via Iterative and Stable Refinement](https://mlsanity.com/paper/2501.13514/) (2025)
- [Validation and Generalizability of Self-Supervised Image Reconstruction Methods for Undersampled MRI](https://mlsanity.com/paper/2201.12535/) (2022)
- [Towards Ultrafast MRI via Extreme k-Space Undersampling and Superresolution](https://mlsanity.com/paper/2103.02940/) (2021)
- [NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems](https://mlsanity.com/paper/2203.00804/) (2022)
- [Subtle Data Crimes: Naively training machine learning algorithms could lead to overly-optimistic results](https://mlsanity.com/paper/2109.08237/) (2021)

## Abstract (arXiv)

Deep neural networks give state-of-the-art accuracy for reconstructing images from few and noisy measurements, a problem arising for example in accelerated magnetic resonance imaging (MRI). However, recent works have raised concerns that deep-learning-based image reconstruction methods are sensitive to perturbations and are less robust than traditional methods: Neural networks (i) may be sensitive to small, yet adversarially-selected perturbations, (ii) may perform poorly under distribution shifts, and (iii) may fail to recover small but important features in an image. In order to understand the sensitivity to such perturbations, in this work, we measure the robustness of different approaches for image reconstruction including trained and un-trained neural networks as well as traditional sparsity-based methods. We find, contrary to prior works, that both trained and un-trained methods are vulnerable to adversarial perturbations. Moreover, both trained and un-trained methods tuned for a particular dataset suffer very similarly from distribution shifts. Finally, we demonstrate that an image reconstruction method that achieves higher reconstruction quality, also performs better in terms of accurately recovering fine details. Our results indicate that the state-of-the-art deep-learning-based image reconstruction methods provide improved performance than traditional methods without compromising robustness.