# Image Compressed Sensing Using Non-local Neural Network

arXiv: https://arxiv.org/abs/2112.03712 · HTML: https://mlsanity.com/paper/2112.03712/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 69 references that are in the map.
- First posted on arXiv 7 Dec 2021.

## Builds on (most cited first, 30 of 30)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [CCNet: Criss-Cross Attention for Semantic Segmentation](https://mlsanity.com/paper/1811.11721/) (2018)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Cross-Scale Internal Graph Neural Network for Image Super-Resolution](https://mlsanity.com/paper/2006.16673/) (2020)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [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)
- [RARE: Image Reconstruction using Deep Priors Learned without Ground Truth](https://mlsanity.com/paper/1912.05854/) (2019)
- [Residual Conv-Deconv Grid Network for Semantic Segmentation](https://mlsanity.com/paper/1707.07958/) (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)
- [Compact Generalized Non-local Network](https://mlsanity.com/paper/1810.13125/) (2018)
- [Deep Graph-Convolutional Image Denoising](https://mlsanity.com/paper/1907.08448/) (2019)
- [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)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [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)
- [Deep neural network based sparse measurement matrix for image compressed sensing](https://mlsanity.com/paper/1806.07026/) (2018)

## Built on by (most cited first, 9 of 9)

- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Revisiting Nonlocal Self-Similarity from Continuous Representation](https://mlsanity.com/paper/2401.00708/) (2024)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [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)
- [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)
- [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)

Deep network-based image Compressed Sensing (CS) has attracted much attention in recent years. However, the existing deep network-based CS schemes either reconstruct the target image in a block-by-block manner that leads to serious block artifacts or train the deep network as a black box that brings about limited insights of image prior knowledge. In this paper, a novel image CS framework using non-local neural network (NL-CSNet) is proposed, which utilizes the non-local self-similarity priors with deep network to improve the reconstruction quality. In the proposed NL-CSNet, two non-local subnetworks are constructed for utilizing the non-local self-similarity priors in the measurement domain and the multi-scale feature domain respectively. Specifically, in the subnetwork of measurement domain, the long-distance dependencies between the measurements of different image blocks are established for better initial reconstruction. Analogically, in the subnetwork of multi-scale feature domain, the affinities between the dense feature representations are explored in the multi-scale space for deep reconstruction. Furthermore, a novel loss function is developed to enhance the coupling between the non-local representations, which also enables an end-to-end training of NL-CSNet. Extensive experiments manifest that NL-CSNet outperforms existing state-of-the-art CS methods, while maintaining fast computational speed.