# COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing

arXiv: https://arxiv.org/abs/2107.07225 · HTML: https://mlsanity.com/paper/2107.07225/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 54 references that are in the map.
- First posted on arXiv 15 Jul 2021.

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

- [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)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [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)
- [One Network to Solve Them All --- Solving Linear Inverse Problems using Deep Projection Models](https://mlsanity.com/paper/1703.09912/) (2017)
- [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)
- [Deep Networks for Compressed Image Sensing](https://mlsanity.com/paper/1707.07119/) (2017)
- [Deep Fully-Connected Networks for Video Compressive Sensing](https://mlsanity.com/paper/1603.04930/) (2016)
- [Convolutional Neural Networks for Non-iterative Reconstruction of Compressively Sensed Images](https://mlsanity.com/paper/1708.04669/) (2017)
- [Simultaneous Fidelity and Regularization Learning for Image Restoration](https://mlsanity.com/paper/1804.04522/) (2018)
- [Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization](https://mlsanity.com/paper/1404.7566/) (2014)
- [Fully Convolutional Measurement Network for Compressive Sensing Image Reconstruction](https://mlsanity.com/paper/1712.01641/) (2017)
- [Rate-Adaptive Neural Networks for Spatial Multiplexers](https://mlsanity.com/paper/1809.02850/) (2018)

## Built on by (most cited first, 30 of 32)

- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [MM-RealSR: Metric Learning based Interactive Modulation for Real-World Super-Resolution](https://mlsanity.com/paper/2205.05065/) (2022)
- [Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imaging](https://mlsanity.com/paper/2109.06548/) (2021)
- [HerosNet: Hyperspectral Explicable Reconstruction and Optimal Sampling Deep Network for Snapshot Compressive Imaging](https://mlsanity.com/paper/2112.06238/) (2021)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Optimization-Inspired Cross-Attention Transformer for Compressive Sensing](https://mlsanity.com/paper/2304.13986/) (2023)
- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [FSOINet: Feature-Space Optimization-Inspired Network for Image Compressive Sensing](https://mlsanity.com/paper/2204.05503/) (2022)
- [TransCL: Transformer Makes Strong and Flexible Compressive Learning](https://mlsanity.com/paper/2207.11972/) (2022)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging](https://mlsanity.com/paper/2505.23180/) (2025)
- [Deep Physics-Guided Unrolling Generalization for Compressed Sensing](https://mlsanity.com/paper/2307.08950/) (2023)
- [LR-CSNet: Low-Rank Deep Unfolding Network for Image Compressive Sensing](https://mlsanity.com/paper/2212.09088/) (2022)
- [PUERT: Probabilistic Under-sampling and Explicable Reconstruction Network for CS-MRI](https://mlsanity.com/paper/2204.11189/) (2022)
- [Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2208.01827/) (2022)
- [Nest-DGIL: Nesterov-optimized Deep Geometric Incremental Learning for CS Image Reconstruction](https://mlsanity.com/paper/2308.03807/) (2023)
- [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)
- [Generalized Tensor Summation Compressive Sensing Network (GTSNET): An Easy to Learn Compressive Sensing Operation](https://mlsanity.com/paper/2108.03167/) (2021)
- [D3C2-Net: Dual-Domain Deep Convolutional Coding Network for Compressive Sensing](https://mlsanity.com/paper/2207.13560/) (2022)
- [Block Modulating Video Compression: An Ultra Low Complexity Image Compression Encoder for Resource Limited Platforms](https://mlsanity.com/paper/2205.03677/) (2022)
- [Hierarchical Perception Adversarial Learning Framework for Compressed Sensing MRI](https://mlsanity.com/paper/2302.10309/) (2023)
- [ICRICS: Iterative Compensation Recovery for Image Compressive Sensing](https://mlsanity.com/paper/2207.09594/) (2022)
- [Recursions Are All You Need: Towards Efficient Deep Unfolding Networks](https://mlsanity.com/paper/2305.05505/) (2023)
- [MB-RACS: Measurement-Bounds-based Rate-Adaptive Image Compressed Sensing Network](https://mlsanity.com/paper/2402.16855/) (2024)
- [Deep Network for Image Compressed Sensing Coding Using Local Structural Sampling](https://mlsanity.com/paper/2402.19111/) (2024)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [A Lightweight Recurrent Learning Network for Sustainable Compressed Sensing](https://mlsanity.com/paper/2304.11674/) (2023)

## Abstract (arXiv)

Recent deep network-based compressive sensing (CS) methods have achieved great success. However, most of them regard different sampling matrices as different independent tasks and need to train a specific model for each target sampling matrix. Such practices give rise to inefficiency in computing and suffer from poor generalization ability. In this paper, we propose a novel COntrollable Arbitrary-Sampling neTwork, dubbed COAST, to solve CS problems of arbitrary-sampling matrices (including unseen sampling matrices) with one single model. Under the optimization-inspired deep unfolding framework, our COAST exhibits good interpretability. In COAST, a random projection augmentation (RPA) strategy is proposed to promote the training diversity in the sampling space to enable arbitrary sampling, and a controllable proximal mapping module (CPMM) and a plug-and-play deblocking (PnP-D) strategy are further developed to dynamically modulate the network features and effectively eliminate the blocking artifacts, respectively. Extensive experiments on widely used benchmark datasets demonstrate that our proposed COAST is not only able to handle arbitrary sampling matrices with one single model but also to achieve state-of-the-art performance with fast speed. The source code is available on https://github.com/jianzhangcs/COAST.