# MsDC-DEQ-Net: Deep Equilibrium Model (DEQ) with Multi-scale Dilated Convolution for Image Compressive Sensing (CS)

arXiv: https://arxiv.org/abs/2401.02884 · HTML: https://mlsanity.com/paper/2401.02884/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 50 references that are in the map.
- First posted on arXiv 5 Jan 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [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)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing](https://mlsanity.com/paper/1702.05743/) (2017)
- [PDCOVIDNet: A Parallel-Dilated Convolutional Neural Network Architecture for Detecting COVID-19 from Chest X-Ray Images](https://mlsanity.com/paper/2007.14777/) (2020)
- [Deep Equilibrium Models for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2201.06931/) (2022)
- [AMPA-Net: Optimization-Inspired Attention Neural Network for Deep Compressed Sensing](https://mlsanity.com/paper/2010.06907/) (2020)
- [CSMCNet: Scalable Video Compressive Sensing Reconstruction with Interpretable Motion Estimation](https://mlsanity.com/paper/2108.01522/) (2021)

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

- [Lipschitz Multiscale Deep Equilibrium Models: A Theoretically Guaranteed and Accelerated Approach](https://mlsanity.com/paper/2602.03297/) (2026)

## Abstract (arXiv)

Compressive sensing (CS) is a technique that enables the recovery of sparse signals using fewer measurements than traditional sampling methods. To address the computational challenges of CS reconstruction, our objective is to develop an interpretable and concise neural network model for reconstructing natural images using CS. We achieve this by mapping one step of the iterative shrinkage thresholding algorithm (ISTA) to a deep network block, representing one iteration of ISTA. To enhance learning ability and incorporate structural diversity, we integrate aggregated residual transformations (ResNeXt) and squeeze-and-excitation (SE) mechanisms into the ISTA block. This block serves as a deep equilibrium layer, connected to a semi-tensor product network (STP-Net) for convenient sampling and providing an initial reconstruction. The resulting model, called MsDC-DEQ-Net, exhibits competitive performance compared to state-of-the-art network-based methods. It significantly reduces storage requirements compared to deep unrolling methods, using only one iteration block instead of multiple iterations. Unlike deep unrolling models, MsDC-DEQ-Net can be iteratively used, gradually improving reconstruction accuracy while considering computation trade-offs. Additionally, the model benefits from multi-scale dilated convolutions, further enhancing performance.