# Learned D-AMP: Principled Neural Network based Compressive Image Recovery

arXiv: https://arxiv.org/abs/1704.06625 · HTML: https://mlsanity.com/paper/1704.06625/

## Key facts

- Cited by 65 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Apr 2017.

## Built on by (most cited first, 30 of 65)

- [Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2201.11793/) (2022)
- [Cold Diffusion: Inverting Arbitrary Image Transforms Without Noise](https://mlsanity.com/paper/2208.09392/) (2022)
- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Robust Equivariant Imaging: a fully unsupervised framework for learning to image from noisy and partial measurements](https://mlsanity.com/paper/2111.12855/) (2021)
- [MIMO Channel Estimation using Score-Based Generative Models](https://mlsanity.com/paper/2204.07122/) (2022)
- [Instance-Optimal Compressed Sensing via Posterior Sampling](https://mlsanity.com/paper/2106.11438/) (2021)
- [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)
- [Theoretical Perspectives on Deep Learning Methods in Inverse Problems](https://mlsanity.com/paper/2206.14373/) (2022)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Generative Diffusion Models for Wireless Networks: Fundamental, Architecture, and State-of-the-Art](https://mlsanity.com/paper/2507.16733/) (2025)
- [Towards Constituting Mathematical Structures for Learning to Optimize](https://mlsanity.com/paper/2305.18577/) (2023)
- [Image Compressed Sensing Using Non-local Neural Network](https://mlsanity.com/paper/2112.03712/) (2021)
- [Image Restoration by Deep Projected GSURE](https://mlsanity.com/paper/2102.02485/) (2021)
- [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)
- [Solving Linear Inverse Problems using Higher-Order Annealed Langevin Diffusion](https://mlsanity.com/paper/2305.05014/) (2023)
- [Dual-Scale Transformer for Large-Scale Single-Pixel Imaging](https://mlsanity.com/paper/2404.05001/) (2024)
- [Diffusion Models for Future Networks and Communications: A Comprehensive Survey](https://mlsanity.com/paper/2508.01586/) (2025)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [NESTANets: Stable, accurate and efficient neural networks for analysis-sparse inverse problems](https://mlsanity.com/paper/2203.00804/) (2022)
- [Fast Hierarchical Deep Unfolding Network for Image Compressed Sensing](https://mlsanity.com/paper/2208.01827/) (2022)
- [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)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [Hybrid ISTA: Unfolding ISTA With Convergence Guarantees Using Free-Form Deep Neural Networks](https://mlsanity.com/paper/2204.11640/) (2022)
- [Successive Interference Cancellation-aided Diffusion Models for Joint Channel Estimation and Data Detection in Low Rank Channel Scenarios](https://mlsanity.com/paper/2501.11229/) (2025)
- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [Two-Stage is Enough: A Concise Deep Unfolding Reconstruction Network for Flexible Video Compressive Sensing](https://mlsanity.com/paper/2201.05810/) (2022)

## Abstract (arXiv)

Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they can run orders of magnitude faster than existing techniques. However, these methods are largely unprincipled black boxes that are difficult to train and often-times specific to a single measurement matrix. It was recently demonstrated that iterative sparse-signal-recovery algorithms can be "unrolled" to form interpretable deep networks. Taking inspiration from this work, we develop a novel neural network architecture that mimics the behavior of the denoising-based approximate message passing (D-AMP) algorithm. We call this new network Learned D-AMP (LDAMP). The LDAMP network is easy to train, can be applied to a variety of different measurement matrices, and comes with a state-evolution heuristic that accurately predicts its performance. Most importantly, it outperforms the state-of-the-art BM3D-AMP and NLR-CS algorithms in terms of both accuracy and run time. At high resolutions, and when used with sensing matrices that have fast implementations, LDAMP runs over 50× faster than BM3D-AMP and hundreds of times faster than NLR-CS.