# LR-CSNet: Low-Rank Deep Unfolding Network for Image Compressive Sensing

arXiv: https://arxiv.org/abs/2212.09088 · HTML: https://mlsanity.com/paper/2212.09088/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 35 references that are in the map.
- First posted on arXiv 18 Dec 2022.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Residual Dense Network for Image Super-Resolution](https://mlsanity.com/paper/1802.08797/) (2018)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Learned Robust PCA: A Scalable Deep Unfolding Approach for High-Dimensional Outlier Detection](https://mlsanity.com/paper/2110.05649/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Tensor Low-Rank Reconstruction for Semantic Segmentation](https://mlsanity.com/paper/2008.00490/) (2020)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [Low-rank and Adaptive Sparse Signal (LASSI) Models for Highly Accelerated Dynamic Imaging](https://mlsanity.com/paper/1611.04069/) (2016)

## Built on by (most cited first, 6 of 6)

- [RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection](https://mlsanity.com/paper/2311.00917/) (2023)
- [CPSeg: Finer-grained Image Semantic Segmentation via Chain-of-Thought Language Prompting](https://mlsanity.com/paper/2310.16069/) (2023)
- [CAS-ViT: Convolutional Additive Self-attention Vision Transformers for Efficient Mobile Applications](https://mlsanity.com/paper/2408.03703/) (2024)
- [RPCANet++: Deep Interpretable Robust PCA for Sparse Object Segmentation](https://mlsanity.com/paper/2508.04190/) (2025)
- [Segment Any Building](https://mlsanity.com/paper/2310.01164/) (2023)
- [Edge Aware Learning for 3D Point Cloud](https://mlsanity.com/paper/2309.13472/) (2023)

## Abstract (arXiv)

Deep unfolding networks (DUNs) have proven to be a viable approach to compressive sensing (CS). In this work, we propose a DUN called low-rank CS network (LR-CSNet) for natural image CS. Real-world image patches are often well-represented by low-rank approximations. LR-CSNet exploits this property by adding a low-rank prior to the CS optimization task. We derive a corresponding iterative optimization procedure using variable splitting, which is then translated to a new DUN architecture. The architecture uses low-rank generation modules (LRGMs), which learn low-rank matrix factorizations, as well as gradient descent and proximal mappings (GDPMs), which are proposed to extract high-frequency features to refine image details. In addition, the deep features generated at each reconstruction stage in the DUN are transferred between stages to boost the performance. Our extensive experiments on three widely considered datasets demonstrate the promising performance of LR-CSNet compared to state-of-the-art methods in natural image CS.