# Deep Compressed Sensing

arXiv: https://arxiv.org/abs/1905.06723 · HTML: https://mlsanity.com/paper/1905.06723/

## Key facts

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

## Built on by (most cited first, 30 of 46)

- [Intermediate Layer Optimization for Inverse Problems using Deep Generative Models](https://mlsanity.com/paper/2102.07364/) (2021)
- [Diffusion Model Based Posterior Sampling for Noisy Linear Inverse Problems](https://mlsanity.com/paper/2211.12343/) (2022)
- [A Theoretical Justification for Image Inpainting using Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2302.01217/) (2023)
- [Learned Gradient Compression for Distributed Deep Learning](https://mlsanity.com/paper/2103.08870/) (2021)
- [Closed-Loop Data Transcription to an LDR via Minimaxing Rate Reduction](https://mlsanity.com/paper/2111.06636/) (2021)
- [Landscape Learning for Neural Network Inversion](https://mlsanity.com/paper/2206.09027/) (2022)
- [Quantized Compressed Sensing with Score-based Generative Models](https://mlsanity.com/paper/2211.13006/) (2022)
- [Provable Compressed Sensing with Generative Priors via Langevin Dynamics](https://mlsanity.com/paper/2102.12643/) (2021)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling](https://mlsanity.com/paper/2407.08256/) (2024)
- [TurbuGAN: An Adversarial Learning Approach to Spatially-Varying Multiframe Blind Deconvolution with Applications to Imaging Through Turbulence](https://mlsanity.com/paper/2203.06764/) (2022)
- [Non-Iterative Recovery from Nonlinear Observations using Generative Models](https://mlsanity.com/paper/2205.15749/) (2022)
- [Multimodal sensor fusion in the latent representation space](https://mlsanity.com/paper/2208.02183/) (2022)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Gradient Importance Learning for Incomplete Observations](https://mlsanity.com/paper/2107.01983/) (2021)
- [Misspecified Phase Retrieval with Generative Priors](https://mlsanity.com/paper/2210.05571/) (2022)
- [Integrating Intermediate Layer Optimization and Projected Gradient Descent for Solving Inverse Problems with Diffusion Models](https://mlsanity.com/paper/2505.20789/) (2025)
- [Latent-Optimized Adversarial Neural Transfer for Sarcasm Detection](https://mlsanity.com/paper/2104.09261/) (2021)
- [ReGuidance: A Simple Diffusion Wrapper for Boosting Sample Quality on Hard Inverse Problems](https://mlsanity.com/paper/2506.10955/) (2025)
- [Differentiable Feature Selection, a Reparameterization Approach](https://mlsanity.com/paper/2107.10030/) (2021)
- [A Compressed Sensing Based Least Squares Approach to Semi-supervised Local Cluster Extraction](https://mlsanity.com/paper/2202.02904/) (2022)
- [Injectivity capacity of ReLU gates](https://mlsanity.com/paper/2410.20646/) (2024)
- [Deep Quantized Representation for Enhanced Reconstruction](https://mlsanity.com/paper/2107.14368/) (2021)
- [Visual Attention Emerges from Recurrent Sparse Reconstruction](https://mlsanity.com/paper/2204.10962/) (2022)
- [Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimension](https://mlsanity.com/paper/2111.14486/) (2021)
- [Residual-Concatenate Neural Network with Deep Regularization Layers for Binary Classification](https://mlsanity.com/paper/2205.12775/) (2022)
- [Learning Single Index Models with Diffusion Priors](https://mlsanity.com/paper/2505.21135/) (2025)
- [Non-Convex Compressed Sensing with Training Data](https://mlsanity.com/paper/2101.08310/) (2021)
- [Learning Generative Prior with Latent Space Sparsity Constraints](https://mlsanity.com/paper/2105.11956/) (2021)
- [One-Bit Compressive Sensing: Can We Go Deep and Blind?](https://mlsanity.com/paper/2203.11278/) (2022)

## 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.