# Robustness of Deep Equilibrium Architectures to Changes in the Measurement Model

arXiv: https://arxiv.org/abs/2211.00531 · HTML: https://mlsanity.com/paper/2211.00531/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 27 references that are in the map.
- First posted on arXiv 1 Nov 2022.

## Builds on (most cited first, 12 of 12)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Deep Learning Techniques for Inverse Problems in Imaging](https://mlsanity.com/paper/2005.06001/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [A Review of Convolutional Neural Networks for Inverse Problems in Imaging](https://mlsanity.com/paper/1710.04011/) (2017)
- [Online Deep Equilibrium Learning for Regularization by Denoising](https://mlsanity.com/paper/2205.13051/) (2022)
- [Model Adaptation for Inverse Problems in Imaging](https://mlsanity.com/paper/2012.00139/) (2020)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)

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

- [Solving Inverse Problems with Model Mismatch using Untrained Neural Networks within Model-based Architectures](https://mlsanity.com/paper/2403.04847/) (2024)
- [Recovering Pulse Waves from Video Using Deep Unrolling and Deep Equilibrium Models](https://mlsanity.com/paper/2503.17269/) (2025)
- [Robustness and Exploration of Variational and Machine Learning Approaches to Inverse Problems: An Overview](https://mlsanity.com/paper/2402.12072/) (2024)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)

## Abstract (arXiv)

Deep model-based architectures (DMBAs) are widely used in imaging inverse problems to integrate physical measurement models and learned image priors. Plug-and-play priors (PnP) and deep equilibrium models (DEQ) are two DMBA frameworks that have received significant attention. The key difference between the two is that the image prior in DEQ is trained by using a specific measurement model, while that in PnP is trained as a general image denoiser. This difference is behind a common assumption that PnP is more robust to changes in the measurement models compared to DEQ. This paper investigates the robustness of DEQ priors to changes in the measurement models. Our results on two imaging inverse problems suggest that DEQ priors trained under mismatched measurement models outperform image denoisers.