# Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing

arXiv: https://arxiv.org/abs/2208.01827 · HTML: https://mlsanity.com/paper/2208.01827/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 57 references that are in the map.
- First posted on arXiv 3 Aug 2022.

## Builds on (most cited first, 21 of 21)

- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (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)
- [Rank Minimization for Snapshot Compressive Imaging](https://mlsanity.com/paper/1807.07837/) (2018)
- [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)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [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)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (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)
- [DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing](https://mlsanity.com/paper/1702.05743/) (2017)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [Multi-Channel Deep Networks for Block-Based Image Compressive Sensing](https://mlsanity.com/paper/1908.11221/) (2019)
- [LAPRAN: A Scalable Laplacian Pyramid Reconstructive Adversarial Network for Flexible Compressive Sensing Reconstruction](https://mlsanity.com/paper/1807.09388/) (2018)
- [Image Compressed Sensing Using Non-local Neural Network](https://mlsanity.com/paper/2112.03712/) (2021)
- [An efficient deep convolutional laplacian pyramid architecture for CS reconstruction at low sampling ratios](https://mlsanity.com/paper/1804.04970/) (2018)
- [Convolutional Video Steganography with Temporal Residual Modeling](https://mlsanity.com/paper/1806.02941/) (2018)

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

- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Sampling Innovation-Based Adaptive Compressive Sensing](https://mlsanity.com/paper/2503.13241/) (2025)
- [Hierarchical Interactive Reconstruction Network For Video Compressive Sensing](https://mlsanity.com/paper/2304.07473/) (2023)
- [WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2411.16336/) (2024)
- [Newton Deep Unfolding for Compressed Sensing](https://mlsanity.com/paper/2609.14391/) (2026)

## Abstract (arXiv)

By integrating certain optimization solvers with deep neural network, deep unfolding network (DUN) has attracted much attention in recent years for image compressed sensing (CS). However, there still exist several issues in existing DUNs: 1) For each iteration, a simple stacked convolutional network is usually adopted, which apparently limits the expressiveness of these models. 2) Once the training is completed, most hyperparameters of existing DUNs are fixed for any input content, which significantly weakens their adaptability. In this paper, by unfolding the Fast Iterative Shrinkage-Thresholding Algorithm (FISTA), a novel fast hierarchical DUN, dubbed FHDUN, is proposed for image compressed sensing, in which a well-designed hierarchical unfolding architecture is developed to cooperatively explore richer contextual prior information in multi-scale spaces. To further enhance the adaptability, series of hyperparametric generation networks are developed in our framework to dynamically produce the corresponding optimal hyperparameters according to the input content. Furthermore, due to the accelerated policy in FISTA, the newly embedded acceleration module makes the proposed FHDUN save more than 50% of the iterative loops against recent DUNs. Extensive CS experiments manifest that the proposed FHDUN outperforms existing state-of-the-art CS methods, while maintaining fewer iterations.