# Neural Proximal Gradient Descent for Compressive Imaging

arXiv: https://arxiv.org/abs/1806.03963 · HTML: https://mlsanity.com/paper/1806.03963/

## Key facts

- Cited by 46 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Jun 2018.

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

- [Learning to Optimize: A Primer and A Benchmark](https://mlsanity.com/paper/2103.12828/) (2021)
- [Deep Equilibrium Architectures for Inverse Problems in Imaging](https://mlsanity.com/paper/2102.07944/) (2021)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [Physics-Driven Deep Learning for Computational Magnetic Resonance Imaging](https://mlsanity.com/paper/2203.12215/) (2022)
- [RU-Net: Regularized Unrolling Network for Scene Graph Generation](https://mlsanity.com/paper/2205.01297/) (2022)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Feasibility-based Fixed Point Networks](https://mlsanity.com/paper/2104.14090/) (2021)
- [Feature Transportation Improves Graph Neural Networks](https://mlsanity.com/paper/2307.16092/) (2023)
- [A review and experimental evaluation of deep learning methods for MRI reconstruction](https://mlsanity.com/paper/2109.08618/) (2021)
- [Towards Constituting Mathematical Structures for Learning to Optimize](https://mlsanity.com/paper/2305.18577/) (2023)
- [Learning A 3D-CNN and Transformer Prior for Hyperspectral Image Super-Resolution](https://mlsanity.com/paper/2111.13923/) (2021)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Improving Generalizability in Limited-Angle CT Reconstruction with Sinogram Extrapolation](https://mlsanity.com/paper/2103.05255/) (2021)
- [Preconditioned Plug-and-Play ADMM with Locally Adjustable Denoiser for Image Restoration](https://mlsanity.com/paper/2110.00493/) (2021)
- [PnP-ReG: Learned Regularizing Gradient for Plug-and-Play Gradient Descent](https://mlsanity.com/paper/2204.13940/) (2022)
- [DRIP: Deep Regularizers for Inverse Problems](https://mlsanity.com/paper/2304.00015/) (2023)
- [A Unified Model for Compressed Sensing MRI Across Undersampling Patterns](https://mlsanity.com/paper/2410.16290/) (2024)
- [Paired Autoencoders for Likelihood-free Estimation in Inverse Problems](https://mlsanity.com/paper/2405.13220/) (2024)
- [Graph Neural Reaction Diffusion Models](https://mlsanity.com/paper/2406.10871/) (2024)
- [Scale-Equivariant Unrolled Neural Networks for Data-Efficient Accelerated MRI Reconstruction](https://mlsanity.com/paper/2204.10436/) (2022)
- [Injectivity capacity of ReLU gates](https://mlsanity.com/paper/2410.20646/) (2024)
- [Sparsity-Driven Parallel Imaging Consistency for Improved Self-Supervised MRI Reconstruction](https://mlsanity.com/paper/2505.24136/) (2025)
- [Deep FlexQP: Accelerated Nonlinear Programming via Deep Unfolding](https://mlsanity.com/paper/2512.01565/) (2025)
- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [GLEAM: Greedy Learning for Large-Scale Accelerated MRI Reconstruction](https://mlsanity.com/paper/2207.08393/) (2022)
- [Deep Unrolling Networks with Recurrent Momentum Acceleration for Nonlinear Inverse Problems](https://mlsanity.com/paper/2307.16120/) (2023)
- [An Over Complete Deep Learning Method for Inverse Problems](https://mlsanity.com/paper/2402.04653/) (2024)
- [A Brief Overview of Optimization-Based Algorithms for MRI Reconstruction Using Deep Learning](https://mlsanity.com/paper/2406.02626/) (2024)
- [Learning Regularization for Graph Inverse Problems](https://mlsanity.com/paper/2408.10436/) (2024)
- [Latent Twins](https://mlsanity.com/paper/2509.20615/) (2025)

## Abstract (arXiv)

Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the recurrent application of proximal gradient algorithm. We learn a proximal map that works well with real images based on residual networks. Contraction of the resulting map is analyzed, and incoherence conditions are investigated that drive the convergence of the iterates. Extensive experiments are carried out under different settings: (a) reconstructing abdominal MRI of pediatric patients from highly undersampled Fourier-space data and (b) superresolving natural face images. Our key findings include: 1. a recurrent ResNet with a single residual block unrolled from an iterative algorithm yields an effective proximal which accurately reveals MR image details. 2. Our architecture significantly outperforms conventional non-recurrent deep ResNets by 2dB SNR; it is also trained much more rapidly. 3. It outperforms state-of-the-art compressed-sensing Wavelet-based methods by 4dB SNR, with 100x speedups in reconstruction time.