# Deep Unfolding Network for Image Compressed Sensing by Content-adaptive Gradient Updating and Deformation-invariant Non-local Modeling

arXiv: https://arxiv.org/abs/2310.10033 · HTML: https://mlsanity.com/paper/2310.10033/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 69 references that are in the map.
- First posted on arXiv 16 Oct 2023.

## Builds on (most cited first, 27 of 27)

- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [End-to-End Object Detection with Transformers](https://mlsanity.com/paper/2005.12872/) (2020)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Asymmetric Non-local Neural Networks for Semantic Segmentation](https://mlsanity.com/paper/1908.07678/) (2019)
- [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)
- [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)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [Deep Graph-Convolutional Image Denoising](https://mlsanity.com/paper/1907.08448/) (2019)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [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)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [Image Compressed Sensing Using Non-local Neural Network](https://mlsanity.com/paper/2112.03712/) (2021)
- [Image Denoising with Graph-Convolutional Neural Networks](https://mlsanity.com/paper/1905.12281/) (2019)
- [An efficient deep convolutional laplacian pyramid architecture for CS reconstruction at low sampling ratios](https://mlsanity.com/paper/1804.04970/) (2018)

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

- [High Frequency Matters: Uncertainty Guided Image Compression with Wavelet Diffusion](https://mlsanity.com/paper/2407.12538/) (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)
- [Dual-Path Hyperprior Informed Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2605.09566/) (2026)
- [Beyond Single Solution: Multi-Hypothesis Collaborative Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2606.03666/) (2026)

## Abstract (arXiv)

Inspired by certain optimization solvers, the deep unfolding network (DUN) has attracted much attention in recent years for image compressed sensing (CS). However, there still exist the following two issues: 1) In existing DUNs, most hyperparameters are usually content independent, which greatly limits their adaptability for different input contents. 2) In each iteration, a plain convolutional neural network is usually adopted, which weakens the perception of wider context prior and therefore depresses the expressive ability. In this paper, inspired by the traditional Proximal Gradient Descent (PGD) algorithm, a novel DUN for image compressed sensing (dubbed DUN-CSNet) is proposed to solve the above two issues. Specifically, for the first issue, a novel content adaptive gradient descent network is proposed, in which a well-designed step size generation sub-network is developed to dynamically allocate the corresponding step sizes for different textures of input image by generating a content-aware step size map, realizing a content-adaptive gradient updating. For the second issue, considering the fact that many similar patches exist in an image but have undergone a deformation, a novel deformation-invariant non-local proximal mapping network is developed, which can adaptively build the long-range dependencies between the nonlocal patches by deformation-invariant non-local modeling, leading to a wider perception on context priors. Extensive experiments manifest that the proposed DUN-CSNet outperforms existing state-of-the-art CS methods by large margins.