# SMUG: Towards robust MRI reconstruction by smoothed unrolling

arXiv: https://arxiv.org/abs/2303.12735 · HTML: https://mlsanity.com/paper/2303.12735/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 24 references that are in the map.
- First posted on arXiv 14 Mar 2023.

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

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Explaining and Harnessing Adversarial Examples](https://mlsanity.com/paper/1412.6572/) (2014)
- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Theoretically Principled Trade-off between Robustness and Accuracy](https://mlsanity.com/paper/1901.08573/) (2019)
- [Certified Adversarial Robustness via Randomized Smoothing](https://mlsanity.com/paper/1902.02918/) (2019)
- [fastMRI: An Open Dataset and Benchmarks for Accelerated MRI](https://mlsanity.com/paper/1811.08839/) (2018)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Rethinking Pre-training and Self-training](https://mlsanity.com/paper/2006.06882/) (2020)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [On instabilities of deep learning in image reconstruction - Does AI come at a cost?](https://mlsanity.com/paper/1902.05300/) (2019)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Framing U-Net via Deep Convolutional Framelets: Application to Sparse-view CT](https://mlsanity.com/paper/1708.08333/) (2017)
- [Deep Residual Learning for Accelerated MRI using Magnitude and Phase Networks](https://mlsanity.com/paper/1804.00432/) (2018)
- [How to Robustify Black-Box ML Models? A Zeroth-Order Optimization Perspective](https://mlsanity.com/paper/2203.14195/) (2022)
- [On Instabilities of Conventional Multi-Coil MRI Reconstruction to Small Adverserial Perturbations](https://mlsanity.com/paper/2102.13066/) (2021)

## Built on by (most cited first, 3 of 3)

- [Robust Physics-based Deep MRI Reconstruction Via Diffusion Purification](https://mlsanity.com/paper/2309.05794/) (2023)
- [Pruning Unrolled Networks (PUN) at Initialization for MRI Reconstruction Improves Generalization](https://mlsanity.com/paper/2412.18668/) (2024)
- [Robust MRI Reconstruction by Smoothed Unrolling (SMUG)](https://mlsanity.com/paper/2312.07784/) (2023)

## Abstract (arXiv)

Although deep learning (DL) has gained much popularity for accelerated magnetic resonance imaging (MRI), recent studies have shown that DL-based MRI reconstruction models could be oversensitive to tiny input perturbations (that are called 'adversarial perturbations'), which cause unstable, low-quality reconstructed images. This raises the question of how to design robust DL methods for MRI reconstruction. To address this problem, we propose a novel image reconstruction framework, termed SMOOTHED UNROLLING (SMUG), which advances a deep unrolling-based MRI reconstruction model using a randomized smoothing (RS)-based robust learning operation. RS, which improves the tolerance of a model against input noises, has been widely used in the design of adversarial defense for image classification. Yet, we find that the conventional design that applies RS to the entire DL process is ineffective for MRI reconstruction. We show that SMUG addresses the above issue by customizing the RS operation based on the unrolling architecture of the DL-based MRI reconstruction model. Compared to the vanilla RS approach and several variants of SMUG, we show that SMUG improves the robustness of MRI reconstruction with respect to a diverse set of perturbation sources, including perturbations to the input measurements, different measurement sampling rates, and different unrolling steps. Code for SMUG will be available at https://github.com/LGM70/SMUG.