# Memory-Augmented Deep Unfolding Network for Compressive Sensing

arXiv: https://arxiv.org/abs/2110.09766 · HTML: https://mlsanity.com/paper/2110.09766/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 54 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [MemNet: A Persistent Memory Network for Image Restoration](https://mlsanity.com/paper/1708.02209/) (2017)
- [A Deep Cascade of Convolutional Neural Networks for Dynamic MR Image Reconstruction](https://mlsanity.com/paper/1704.02422/) (2017)
- [Recurrent Squeeze-and-Excitation Context Aggregation Net for Single Image Deraining](https://mlsanity.com/paper/1807.05698/) (2018)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [A Deep Learning Approach to Structured Signal Recovery](https://mlsanity.com/paper/1508.04065/) (2015)
- [Group-based Sparse Representation for Image Restoration](https://mlsanity.com/paper/1405.3351/) (2014)
- [Non-Local Color Image Denoising with Convolutional Neural Networks](https://mlsanity.com/paper/1611.06757/) (2016)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Deep Image Demosaicking using a Cascade of Convolutional Residual Denoising Networks](https://mlsanity.com/paper/1803.05215/) (2018)
- [Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imaging](https://mlsanity.com/paper/2109.06548/) (2021)
- [Multi-Channel Deep Networks for Block-Based Image Compressive Sensing](https://mlsanity.com/paper/1908.11221/) (2019)
- [Deep Fully-Connected Networks for Video Compressive Sensing](https://mlsanity.com/paper/1603.04930/) (2016)
- [Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization](https://mlsanity.com/paper/1404.7566/) (2014)

## Built on by (most cited first, 30 of 38)

- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [HerosNet: Hyperspectral Explicable Reconstruction and Optimal Sampling Deep Network for Snapshot Compressive Imaging](https://mlsanity.com/paper/2112.06238/) (2021)
- [Memory-augmented Deep Unfolding Network for Guided Image Super-resolution](https://mlsanity.com/paper/2203.04960/) (2022)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [Optimization-Inspired Cross-Attention Transformer for Compressive Sensing](https://mlsanity.com/paper/2304.13986/) (2023)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [TransCL: Transformer Makes Strong and Flexible Compressive Learning](https://mlsanity.com/paper/2207.11972/) (2022)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [Deep Unfolding Multi-modal Image Fusion Network via Attribution Analysis](https://mlsanity.com/paper/2502.01467/) (2025)
- [Dual-Scale Transformer for Large-Scale Single-Pixel Imaging](https://mlsanity.com/paper/2404.05001/) (2024)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2208.01827/) (2022)
- [Deep Unfolding Network for Image Compressed Sensing by Content-adaptive Gradient Updating and Deformation-invariant Non-local Modeling](https://mlsanity.com/paper/2310.10033/) (2023)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [Panchromatic and Multispectral Image Fusion via Alternating Reverse Filtering Network](https://mlsanity.com/paper/2210.08181/) (2022)
- [ℓ1DecNet+: A new architecture framework by ℓ1 decomposition and iteration unfolding for sparse feature segmentation](https://mlsanity.com/paper/2203.02690/) (2022)
- [Score-based Generative Priors Guided Model-driven Network for MRI Reconstruction](https://mlsanity.com/paper/2405.02958/) (2024)
- [Model-Guided Multi-Contrast Deep Unfolding Network for MRI Super-resolution Reconstruction](https://mlsanity.com/paper/2209.07030/) (2022)
- [A Compound Gaussian Least Squares Algorithm and Unrolled Network for Linear Inverse Problems](https://mlsanity.com/paper/2305.11120/) (2023)
- [MCU-Net: A Multi-prior Collaborative Deep Unfolding Network with Gates-controlled Spatial Attention for Accelerated MR Image Reconstruction](https://mlsanity.com/paper/2402.03383/) (2024)
- [ICRICS: Iterative Compensation Recovery for Image Compressive Sensing](https://mlsanity.com/paper/2207.09594/) (2022)
- [Deep Regularized Compound Gaussian Network for Solving Linear Inverse Problems](https://mlsanity.com/paper/2311.17248/) (2023)
- [On Generalization Bounds for Deep Compound Gaussian Neural Networks](https://mlsanity.com/paper/2402.13106/) (2024)
- [Deep Network for Image Compressed Sensing Coding Using Local Structural Sampling](https://mlsanity.com/paper/2402.19111/) (2024)
- [MVMS-RCN: A Dual-Domain Unfolding CT Reconstruction with Multi-sparse-view and Multi-scale Refinement-correction](https://mlsanity.com/paper/2405.17141/) (2024)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [Sampling Innovation-Based Adaptive Compressive Sensing](https://mlsanity.com/paper/2503.13241/) (2025)
- [Deep LoRA-Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2602.18697/) (2026)

## Abstract (arXiv)

Mapping a truncated optimization method into a deep neural network, deep unfolding network (DUN) has attracted growing attention in compressive sensing (CS) due to its good interpretability and high performance. Each stage in DUNs corresponds to one iteration in optimization. By understanding DUNs from the perspective of the human brain's memory processing, we find there exists two issues in existing DUNs. One is the information between every two adjacent stages, which can be regarded as short-term memory, is usually lost seriously. The other is no explicit mechanism to ensure that the previous stages affect the current stage, which means memory is easily forgotten. To solve these issues, in this paper, a novel DUN with persistent memory for CS is proposed, dubbed Memory-Augmented Deep Unfolding Network (MADUN). We design a memory-augmented proximal mapping module (MAPMM) by combining two types of memory augmentation mechanisms, namely High-throughput Short-term Memory (HSM) and Cross-stage Long-term Memory (CLM). HSM is exploited to allow DUNs to transmit multi-channel short-term memory, which greatly reduces information loss between adjacent stages. CLM is utilized to develop the dependency of deep information across cascading stages, which greatly enhances network representation capability. Extensive CS experiments on natural and MR images show that with the strong ability to maintain and balance information our MADUN outperforms existing state-of-the-art methods by a large margin. The source code is available at https://github.com/jianzhangcs/MADUN/.