# Proximal Algorithm Unrolling: Flexible and Efficient Reconstruction Networks for Single-Pixel Imaging

arXiv: https://arxiv.org/abs/2505.23180 · HTML: https://mlsanity.com/paper/2505.23180/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 71 references that are in the map.
- First posted on arXiv 29 May 2025.

## Builds on (most cited first, 30 of 31)

- [Restormer: Efficient Transformer for High-Resolution Image Restoration](https://mlsanity.com/paper/2111.09881/) (2021)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [FFDNet: Toward a Fast and Flexible Solution for CNN based Image Denoising](https://mlsanity.com/paper/1710.04026/) (2017)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Algorithm Unrolling: Interpretable, Efficient Deep Learning for Signal and Image Processing](https://mlsanity.com/paper/1912.10557/) (2019)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [MoDL: Model Based Deep Learning Architecture for Inverse Problems](https://mlsanity.com/paper/1712.02862/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Deep Generalized Unfolding Networks for Image Restoration](https://mlsanity.com/paper/2204.13348/) (2022)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Plug-and-Play Methods for Integrating Physical and Learned Models in Computational Imaging](https://mlsanity.com/paper/2203.17061/) (2022)
- [Denoising Prior Driven Deep Neural Network for Image Restoration](https://mlsanity.com/paper/1801.06756/) (2018)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [From Denoising to Compressed Sensing](https://mlsanity.com/paper/1406.4175/) (2014)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Learned D-AMP: Principled Neural Network based Compressive Image Recovery](https://mlsanity.com/paper/1704.06625/) (2017)
- [Scalable Plug-and-Play ADMM with Convergence Guarantees](https://mlsanity.com/paper/2006.03224/) (2020)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [Block Coordinate Regularization by Denoising](https://mlsanity.com/paper/1905.05113/) (2019)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing](https://mlsanity.com/paper/1702.05743/) (2017)
- [What's in a Prior? Learned Proximal Networks for Inverse Problems](https://mlsanity.com/paper/2310.14344/) (2023)
- [Deep Unfolding of a Proximal Interior Point Method for Image Restoration](https://mlsanity.com/paper/1812.04276/) (2018)
- [CSformer: Bridging Convolution and Transformer for Compressive Sensing](https://mlsanity.com/paper/2112.15299/) (2021)
- [Stochastic Deep Restoration Priors for Imaging Inverse Problems](https://mlsanity.com/paper/2410.02057/) (2024)
- [Optimization-Inspired Cross-Attention Transformer for Compressive Sensing](https://mlsanity.com/paper/2304.13986/) (2023)
- [Robust Stochastically-Descending Unrolled Networks](https://mlsanity.com/paper/2312.15788/) (2023)
- [Deep Optics for Video Snapshot Compressive Imaging](https://mlsanity.com/paper/2404.05274/) (2024)

## Built on by (most cited first, 8 of 8)

- [Scalable Deep Unfolding of Conic Optimizers](https://mlsanity.com/paper/2606.13825/) (2026)
- [Unrolled Graph Neural Networks for Constrained Optimization](https://mlsanity.com/paper/2509.17156/) (2025)
- [Physics-guided Deep Unfolding Network for Enhanced Kronecker Compressive sensing](https://mlsanity.com/paper/2508.09528/) (2025)
- [Unrolled Neural Networks for Constrained Optimization](https://mlsanity.com/paper/2601.17274/) (2026)
- [Compressive sensing inspired self-supervised single-pixel imaging](https://mlsanity.com/paper/2603.29732/) (2026)
- [Deep Probabilistic Unfolding for Quantized Compressive Sensing](https://mlsanity.com/paper/2605.11475/) (2026)
- [Variational Deep Unfolding with Mamba-Based Nonlocal Modeling for Underwater Image Enhancement](https://mlsanity.com/paper/2606.14781/) (2026)
- [The Lift Spectrum: How Measurement-to-Space Adaptivity Shapes Robustness in Image-Free Single-Pixel Sensing](https://mlsanity.com/paper/2607.22077/) (2026)

## Abstract (arXiv)

Deep-unrolling and plug-and-play (PnP) approaches have become the de-facto standard solvers for single-pixel imaging (SPI) inverse problem. PnP approaches, a class of iterative algorithms where regularization is implicitly performed by an off-the-shelf deep denoiser, are flexible for varying compression ratios (CRs) but are limited in reconstruction accuracy and speed. Conversely, unrolling approaches, a class of multi-stage neural networks where a truncated iterative optimization process is transformed into an end-to-end trainable network, typically achieve better accuracy with faster inference but require fine-tuning or even retraining when CR changes. In this paper, we address the challenge of integrating the strengths of both classes of solvers. To this end, we design an efficient deep image restorer (DIR) for the unrolling of HQS (half quadratic splitting) and ADMM (alternating direction method of multipliers). More importantly, a general proximal trajectory (PT) loss function is proposed to train HQS/ADMM-unrolling networks such that learned DIR approximates the proximal operator of an ideal explicit restoration regularizer. Extensive experiments demonstrate that, the resulting proximal unrolling networks can not only flexibly handle varying CRs with a single model like PnP algorithms, but also outperform previous CR-specific unrolling networks in both reconstruction accuracy and speed. Source codes and models are available at https://github.com/pwangcs/ProxUnroll.