mlsanityData to 14 Oct 2026

Deep Compressed Sensing

arXiv 1905.06723 ↗First posted 16 May 2019cs.LG eess.SP stat.MLcited by 46

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Abstract (arXiv)

Compressed sensing (CS) provides an elegant framework for recovering sparse signals from compressed measurements. For example, CS can exploit the structure of natural images and recover an image from only a few random measurements. CS is flexible and data efficient, but its application has been restricted by the strong assumption of sparsity and costly reconstruction process. A recent approach that combines CS with neural network generators has removed the constraint of sparsity, but reconstruction remains slow. Here we propose a novel framework that significantly improves both the performance and speed of signal recovery by jointly training a generator and the optimisation process for reconstruction via meta-learning. We explore training the measurements with different objectives, and derive a family of models based on minimising measurement errors. We show that Generative Adversarial Nets (GANs) can be viewed as a special case in this family of models. Borrowing insights from the CS perspective, we develop a novel way of improving GANs using gradient information from the discriminator.

Key facts. Cited by 46 papers in the map (data through 14 Oct 2026). First posted on arXiv 16 May 2019.

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 15; 2022: 14; 2023: 5; 2024: 5; 2025: 5; 2026: 2.

46 papers.

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  1. 2021Intermediate Layer Optimization for Inverse Problems using Deep Generative Modelscited by 70
  2. 2022Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problemscited by 60
  3. 2023A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Modelscited by 37
  4. 2021Learned Gradient Compression for Distributed Deep Learningcited by 20
  5. 2021Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reductioncited by 17
  6. 2022Landscape Learning for Neural Network Inversioncited by 15
  7. 2022Quantized Compressed Sensing with Score-based Generative Modelscited by 15
  8. 2021Provable Compressed Sensing with Generative Priors via Langevin Dynamicscited by 14
  9. 2021CSformer: Bridging Convolution and Transformer for Compressive Sensingcited by 14
  10. 2024Adaptive Compressed Sensing with Diffusion-Based Posterior Samplingcited by 13
  11. 2022TurbuGAN: An Adversarial Learning Approach to Spatially-Varying Multiframe Blind Deconvolution with Applications to Imaging Through Turbulencecited by 11
  12. 2022Non-Iterative Recovery from Nonlinear Observations using Generative Modelscited by 9
34 more
  1. 2022Multimodal sensor fusion in the latent representation spacecited by 9
  2. 2023Self-Supervised Scalable Deep Compressed Sensingcited by 8
  3. 2021Gradient Importance Learning for Incomplete Observationscited by 7
  4. 2022Misspecified Phase Retrieval with Generative Priorscited by 7
  5. 2025Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Modelscited by 7
  6. 2021Latent-Optimized Adversarial Neural Transfer for Sarcasm Detectioncited by 6
  7. 2025ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problemscited by 5
  8. 2021Differentiable Feature Selection, a Reparameterization Approachcited by 4
  9. 2022A Compressed Sensing Based Least Squares Approach to Semi-supervised Local Cluster Extractioncited by 4
  10. 2024Injectivity capacity of ReLU gatescited by 4
  11. 2021Deep Quantized Representation for Enhanced Reconstructioncited by 3
  12. 2022Visual Attention Emerges from Recurrent Sparse Reconstructioncited by 3
  13. 2021Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimensioncited by 2
  14. 2022Residual-Concatenate Neural Network with Deep Regularization Layers for Binary Classificationcited by 2
  15. 2025Learning Single Index Models with Diffusion Priorscited by 2
  16. 2021Non-Convex Compressed Sensing with Training Datacited by 1
  17. 2021Learning Generative Prior with Latent Space Sparsity Constraintscited by 1
  18. 2022One-Bit Compressive Sensing: Can We Go Deep and Blind?cited by 1
  19. 2022Robust Deep Compressive Sensing with Recurrent-Residual Structural Constraintscited by 1
  20. 2022MetaDIP: Accelerating Deep Image Prior with Meta Learningcited by 1
  21. 2023On the Fine-Grained Hardness of Inverting Generative Modelscited by 1
  22. 2024Generalized Compressed Sensing for Image Reconstruction with Diffusion Probabilistic Modelscited by 1
  23. 2025Lifting Biomolecular Data Acquisitioncited by 1
  24. 2026Outlier-Robust Diffusion Solvers for Inverse Problemscited by 1
  25. 2021Scalable Deep Compressive Sensingcited by 0
  26. 2021OpenICS: Open Image Compressive Sensing Toolbox and Benchmarkcited by 0
  27. 2021Generative Model Adversarial Training for Deep Compressed Sensingcited by 0
  28. 2022MrSARP: A Hierarchical Deep Generative Prior for SAR Image Super-resolutioncited by 0
  29. 2023Learning Trees of ℓ0-Minimization Problemscited by 0
  30. 2023Counterfactual Outcome Prediction using Structured State Space Modelcited by 0
  31. 2024Compressed Sensor Caching and Collaborative Sparse Data Recovery with Anchor Alignmentcited by 0
  32. 2024Towards Lensless Image Deblurring with Prior-Embedded Implicit Neural Representations in the Low-Data Regimecited by 0
  33. 2025Gibbs randomness-compression propositioncited by 0
  34. 2026Flow-Based Generative Modeling for Optimizing Sampling Policies in Compressed Sensing Applicationscited by 0