# CSformer: Bridging Convolution and Transformer for Compressive Sensing

arXiv: https://arxiv.org/abs/2112.15299 · HTML: https://mlsanity.com/paper/2112.15299/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 86 references that are in the map.
- First posted on arXiv 31 Dec 2021.

## Builds on (most cited first, 30 of 40)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Feature Pyramid Networks for Object Detection](https://mlsanity.com/paper/1612.03144/) (2016)
- [Non-local Neural Networks](https://mlsanity.com/paper/1711.07971/) (2017)
- [SwinIR: Image Restoration Using Swin Transformer](https://mlsanity.com/paper/2108.10257/) (2021)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Pre-Trained Image Processing Transformer](https://mlsanity.com/paper/2012.00364/) (2020)
- [Uformer: A General U-Shaped Transformer for Image Restoration](https://mlsanity.com/paper/2106.03106/) (2021)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [A Survey on Visual Transformer](https://mlsanity.com/paper/2012.12556/) (2020)
- [CoAtNet: Marrying Convolution and Attention for All Data Sizes](https://mlsanity.com/paper/2106.04803/) (2021)
- [ConViT: Improving Vision Transformers with Soft Convolutional Inductive Biases](https://mlsanity.com/paper/2103.10697/) (2021)
- [Early Convolutions Help Transformers See Better](https://mlsanity.com/paper/2106.14881/) (2021)
- [Learning Texture Transformer Network for Image Super-Resolution](https://mlsanity.com/paper/2006.04139/) (2020)
- [CoTr: Efficiently Bridging CNN and Transformer for 3D Medical Image Segmentation](https://mlsanity.com/paper/2103.03024/) (2021)
- [Conformer: Local Features Coupling Global Representations for Visual Recognition](https://mlsanity.com/paper/2105.03889/) (2021)
- [TransGAN: Two Pure Transformers Can Make One Strong GAN, and That Can Scale Up](https://mlsanity.com/paper/2102.07074/) (2021)
- [Non-local Attention Optimized Deep Image Compression](https://mlsanity.com/paper/1904.09757/) (2019)
- [Plug-and-Play Algorithms for Large-scale Snapshot Compressive Imaging](https://mlsanity.com/paper/2003.13654/) (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)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Dense Attention Fluid Network for Salient Object Detection in Optical Remote Sensing Images](https://mlsanity.com/paper/2011.13144/) (2020)
- [Deep Compressed Sensing](https://mlsanity.com/paper/1905.06723/) (2019)
- [Group-based Sparse Representation for Image Restoration](https://mlsanity.com/paper/1405.3351/) (2014)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Towards Unsupervised Deep Image Enhancement with Generative Adversarial Network](https://mlsanity.com/paper/2012.15020/) (2020)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)

## Built on by (most cited first, 14 of 14)

- [SS-MAE: Spatial-Spectral Masked Auto-Encoder for Multi-Source Remote Sensing Image Classification](https://mlsanity.com/paper/2311.04442/) (2023)
- [Affective Behaviour Analysis via Integrating Multi-Modal Knowledge](https://mlsanity.com/paper/2403.10825/) (2024)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [Exploring Resolution Fields for Scalable Image Compression with Uncertainty Guidance](https://mlsanity.com/paper/2306.08941/) (2023)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [Uformer-ICS: A U-Shaped Transformer for Image Compressive Sensing Service](https://mlsanity.com/paper/2209.01763/) (2022)
- [Consistent Diffusion: Denoising Diffusion Model with Data-Consistent Training for Image Restoration](https://mlsanity.com/paper/2412.12550/) (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)
- [Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detection](https://mlsanity.com/paper/2509.07654/) (2025)
- [Deep LoRA-Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2602.18697/) (2026)
- [WTDUN: Wavelet Tree-Structured Sampling and Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2411.16336/) (2024)
- [Beyond Single Solution: Multi-Hypothesis Collaborative Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2606.03666/) (2026)

## Abstract (arXiv)

Convolution neural networks (CNNs) have succeeded in compressive image sensing. However, due to the inductive bias of locality and weight sharing, the convolution operations demonstrate the intrinsic limitations in modeling the long-range dependency. Transformer, designed initially as a sequence-to-sequence model, excels at capturing global contexts due to the self-attention-based architectures even though it may be equipped with limited localization abilities. This paper proposes CSformer, a hybrid framework that integrates the advantages of leveraging both detailed spatial information from CNN and the global context provided by transformer for enhanced representation learning. The proposed approach is an end-to-end compressive image sensing method, composed of adaptive sampling and recovery. In the sampling module, images are measured block-by-block by the learned sampling matrix. In the reconstruction stage, the measurement is projected into dual stems. One is the CNN stem for modeling the neighborhood relationships by convolution, and the other is the transformer stem for adopting global self-attention mechanism. The dual branches structure is concurrent, and the local features and global representations are fused under different resolutions to maximize the complementary of features. Furthermore, we explore a progressive strategy and window-based transformer block to reduce the parameter and computational complexity. The experimental results demonstrate the effectiveness of the dedicated transformer-based architecture for compressive sensing, which achieves superior performance compared to state-of-the-art methods on different datasets.