# Deep Equilibrium Models for Video Snapshot Compressive Imaging

arXiv: https://arxiv.org/abs/2201.06931 · HTML: https://mlsanity.com/paper/2201.06931/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 51 references that are in the map.
- First posted on arXiv 18 Jan 2022.

## Builds on (most cited first, 28 of 28)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [The 2017 DAVIS Challenge on Video Object Segmentation](https://mlsanity.com/paper/1704.00675/) (2017)
- [Universal Transformers](https://mlsanity.com/paper/1807.03819/) (2018)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [The Reversible Residual Network: Backpropagation Without Storing Activations](https://mlsanity.com/paper/1707.04585/) (2017)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Spectral Norm Regularization for Improving the Generalizability of Deep Learning](https://mlsanity.com/paper/1705.10941/) (2017)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [Plug-and-Play Priors for Bright Field Electron Tomography and Sparse Interpolation](https://mlsanity.com/paper/1512.07331/) (2015)
- [Plug-and-Play Algorithms for Large-scale Snapshot Compressive Imaging](https://mlsanity.com/paper/2003.13654/) (2020)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Coded aperture compressive temporal imaging](https://mlsanity.com/paper/1302.2575/) (2013)
- [GAP-net for Snapshot Compressive Imaging](https://mlsanity.com/paper/2012.08364/) (2020)
- [Trellis Networks for Sequence Modeling](https://mlsanity.com/paper/1810.06682/) (2018)
- [Plug-and-Play Algorithms for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2101.04822/) (2021)
- [Recurrent Stacking of Layers for Compact Neural Machine Translation Models](https://mlsanity.com/paper/1807.05353/) (2018)
- [Tuning-free Plug-and-Play Proximal Algorithm for Inverse Imaging Problems](https://mlsanity.com/paper/2002.09611/) (2020)
- [Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imaging](https://mlsanity.com/paper/2109.06548/) (2021)
- [Memory-Efficient Network for Large-scale Video Compressive Sensing](https://mlsanity.com/paper/2103.03089/) (2021)
- [MetaSCI: Scalable and Adaptive Reconstruction for Video Compressive Sensing](https://mlsanity.com/paper/2103.01786/) (2021)
- [Adaptive Deep PnP Algorithm for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2201.05483/) (2022)
- [Two-Stage is Enough: A Concise Deep Unfolding Reconstruction Network for Flexible Video Compressive Sensing](https://mlsanity.com/paper/2201.05810/) (2022)
- [Revisit Dictionary Learning for Video Compressive Sensing under the Plug-and-Play Framework](https://mlsanity.com/paper/2110.04966/) (2021)

## Built on by (most cited first, 5 of 5)

- [Subhomogeneous Deep Equilibrium Models](https://mlsanity.com/paper/2403.00720/) (2024)
- [Self-Supervised Deep Equilibrium Models for Inverse Problems with Theoretical Guarantees](https://mlsanity.com/paper/2210.03837/) (2022)
- [MsDC-DEQ-Net: Deep Equilibrium Model (DEQ) with Multi-scale Dilated Convolution for Image Compressive Sensing (CS)](https://mlsanity.com/paper/2401.02884/) (2024)
- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)
- [Mathematical Cookbook for Snapshot Compressive Imaging](https://mlsanity.com/paper/2202.07437/) (2022)

## Abstract (arXiv)

The ability of snapshot compressive imaging (SCI) systems to efficiently capture high-dimensional (HD) data has led to an inverse problem, which consists of recovering the HD signal from the compressed and noisy measurement. While reconstruction algorithms grow fast to solve it with the recent advances of deep learning, the fundamental issue of accurate and stable recovery remains. To this end, we propose deep equilibrium models (DEQ) for video SCI, fusing data-driven regularization and stable convergence in a theoretically sound manner. Each equilibrium model implicitly learns a nonexpansive operator and analytically computes the fixed point, thus enabling unlimited iterative steps and infinite network depth with only a constant memory requirement in training and testing. Specifically, we demonstrate how DEQ can be applied to two existing models for video SCI reconstruction: recurrent neural networks (RNN) and Plug-and-Play (PnP) algorithms. On a variety of datasets and real data, both quantitative and qualitative evaluations of our results demonstrate the effectiveness and stability of our proposed method. The code and models are available at: https://github.com/IndigoPurple/DEQSCI .