# Deep Physics-Guided Unrolling Generalization for Compressed Sensing

arXiv: https://arxiv.org/abs/2307.08950 · HTML: https://mlsanity.com/paper/2307.08950/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 98 references that are in the map.
- First posted on arXiv 18 Jul 2023.

## Builds on (most cited first, 30 of 33)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Image Super-Resolution Using Very Deep Residual Channel Attention Networks](https://mlsanity.com/paper/1807.02758/) (2018)
- [Real-Time Single Image and Video Super-Resolution Using an Efficient Sub-Pixel Convolutional Neural Network](https://mlsanity.com/paper/1609.05158/) (2016)
- [Multi-Stage Progressive Image Restoration](https://mlsanity.com/paper/2102.02808/) (2021)
- [Plug-and-Play Image Restoration with Deep Denoiser Prior](https://mlsanity.com/paper/2008.13751/) (2020)
- [Learning Deep CNN Denoiser Prior for Image Restoration](https://mlsanity.com/paper/1704.03264/) (2017)
- [Deep Unfolding Network for Image Super-Resolution](https://mlsanity.com/paper/2003.10428/) (2020)
- [Learned Primal-dual Reconstruction](https://mlsanity.com/paper/1707.06474/) (2017)
- [Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration](https://mlsanity.com/paper/1508.02848/) (2015)
- [Interpreting Super-Resolution Networks with Local Attribution Maps](https://mlsanity.com/paper/2011.11036/) (2020)
- [Equivariant Imaging: Learning Beyond the Range Space](https://mlsanity.com/paper/2103.14756/) (2021)
- [FISTA-Net: Learning A Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging](https://mlsanity.com/paper/2008.02683/) (2020)
- [AMP-Net: Denoising based Deep Unfolding for Compressive Image Sensing](https://mlsanity.com/paper/2004.10078/) (2020)
- [Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning](https://mlsanity.com/paper/1904.02816/) (2019)
- [A Deep Learning Approach to Structured Signal Recovery](https://mlsanity.com/paper/1508.04065/) (2015)
- [Group-based Sparse Representation for Image Restoration](https://mlsanity.com/paper/1405.3351/) (2014)
- [Non-Local Color Image Denoising with Convolutional Neural Networks](https://mlsanity.com/paper/1611.06757/) (2016)
- [ISTA-Net++: Flexible Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2103.11554/) (2021)
- [Memory-Augmented Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2110.09766/) (2021)
- [COAST: COntrollable Arbitrary-Sampling NeTwork for Compressive Sensing](https://mlsanity.com/paper/2107.07225/) (2021)
- [Deep Image Demosaicking using a Cascade of Convolutional Residual Denoising Networks](https://mlsanity.com/paper/1803.05215/) (2018)
- [Dense Deep Unfolding Network with 3D-CNN Prior for Snapshot Compressive Imaging](https://mlsanity.com/paper/2109.06548/) (2021)
- [Deep Decomposition Learning for Inverse Imaging Problems](https://mlsanity.com/paper/1911.11028/) (2019)
- [Learning to Invert: Signal Recovery via Deep Convolutional Networks](https://mlsanity.com/paper/1701.03891/) (2017)
- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [Dynamic Path-Controllable Deep Unfolding Network for Compressive Sensing](https://mlsanity.com/paper/2306.16060/) (2023)

## Built on by (most cited first, 7 of 7)

- [Invertible Diffusion Models for Compressed Sensing](https://mlsanity.com/paper/2403.17006/) (2024)
- [ResVR: Joint Rescaling and Viewport Rendering of Omnidirectional Images](https://mlsanity.com/paper/2404.16825/) (2024)
- [NPN: Non-Linear Projections of the Null-Space for Imaging Inverse Problems](https://mlsanity.com/paper/2510.01608/) (2025)
- [Using Powerful Prior Knowledge of Diffusion Model in Deep Unfolding Networks for Image Compressive Sensing](https://mlsanity.com/paper/2503.08429/) (2025)
- [Sampling Innovation-Based Adaptive Compressive Sensing](https://mlsanity.com/paper/2503.13241/) (2025)
- [Radiative-Structured Neural Operator for Continuous Spectral Super-Resolution](https://mlsanity.com/paper/2511.17895/) (2025)
- [LRDUN: A Low-Rank Deep Unfolding Network for Efficient Spectral Compressive Imaging](https://mlsanity.com/paper/2511.18513/) (2025)

## Abstract (arXiv)

By absorbing the merits of both the model- and data-driven methods, deep physics-engaged learning scheme achieves high-accuracy and interpretable image reconstruction. It has attracted growing attention and become the mainstream for inverse imaging tasks. Focusing on the image compressed sensing (CS) problem, we find the intrinsic defect of this emerging paradigm, widely implemented by deep algorithm-unrolled networks, in which more plain iterations involving real physics will bring enormous computation cost and long inference time, hindering their practical application. A novel deep Physics-guided unRolled recovery Learning (PRL) framework is proposed by generalizing the traditional iterative recovery model from image domain (ID) to the high-dimensional feature domain (FD). A compact multiscale unrolling architecture is then developed to enhance the network capacity and keep real-time inference speeds. Taking two different perspectives of optimization and range-nullspace decomposition, instead of building an algorithm-specific unrolled network, we provide two implementations: PRL-PGD and PRL-RND. Experiments exhibit the significant performance and efficiency leading of PRL networks over other state-of-the-art methods with a large potential for further improvement and real application to other inverse imaging problems or optimization models.