# NL-CS Net: Deep Learning with Non-Local Prior for Image Compressive Sensing

arXiv: https://arxiv.org/abs/2305.03899 · HTML: https://mlsanity.com/paper/2305.03899/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 56 references that are in the map.
- First posted on arXiv 6 May 2023.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [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)
- [Deep Learning for Image Super-resolution: A Survey](https://mlsanity.com/paper/1902.06068/) (2019)
- [Non-Local Recurrent Network for Image Restoration](https://mlsanity.com/paper/1806.02919/) (2018)
- [Deep learning for undersampled MRI reconstruction](https://mlsanity.com/paper/1709.02576/) (2017)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [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)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (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)
- [COLA-Net: Collaborative Attention Network for Image Restoration](https://mlsanity.com/paper/2103.05961/) (2021)
- [Fully Convolutional Measurement Network for Compressive Sensing Image Reconstruction](https://mlsanity.com/paper/1712.01641/) (2017)
- [A Deep Learning Approach to Block-based Compressed Sensing of Images](https://mlsanity.com/paper/1606.01519/) (2016)
- [Optimized Projections for Compressed Sensing via Direct Mutual Coherence Minimization](https://mlsanity.com/paper/1508.03117/) (2015)

## Abstract (arXiv)

Deep learning has been applied to compressive sensing (CS) of images successfully in recent years. However, existing network-based methods are often trained as the black box, in which the lack of prior knowledge is often the bottleneck for further performance improvement. To overcome this drawback, this paper proposes a novel CS method using non-local prior which combines the interpretability of the traditional optimization methods with the speed of network-based methods, called NL-CS Net. We unroll each phase from iteration of the augmented Lagrangian method solving non-local and sparse regularized optimization problem by a network. NL-CS Net is composed of the up-sampling module and the recovery module. In the up-sampling module, we use learnable up-sampling matrix instead of a predefined one. In the recovery module, patch-wise non-local network is employed to capture long-range feature correspondences. Important parameters involved (e.g. sampling matrix, nonlinear transforms, shrinkage thresholds, step size, etc.) are learned end-to-end, rather than hand-crafted. Furthermore, to facilitate practical implementation, orthogonal and binary constraints on the sampling matrix are simultaneously adopted. Extensive experiments on natural images and magnetic resonance imaging (MRI) demonstrate that the proposed method outperforms the state-of-the-art methods while maintaining great interpretability and speed.