# prDeep: Robust Phase Retrieval with a Flexible Deep Network

arXiv: https://arxiv.org/abs/1803.00212 · HTML: https://mlsanity.com/paper/1803.00212/

## Key facts

- Cited by 47 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Mar 2018.

## Built on by (most cited first, 30 of 47)

- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [DOLCE: A Model-Based Probabilistic Diffusion Framework for Limited-Angle CT Reconstruction](https://mlsanity.com/paper/2211.12340/) (2022)
- [Recovery Analysis for Plug-and-Play Priors using the Restricted Eigenvalue Condition](https://mlsanity.com/paper/2106.03668/) (2021)
- [Online Deep Equilibrium Learning for Regularization by Denoising](https://mlsanity.com/paper/2205.13051/) (2022)
- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees](https://mlsanity.com/paper/2101.09379/) (2021)
- [Plug-and-Play image restoration with Stochastic deNOising REgularization](https://mlsanity.com/paper/2402.01779/) (2024)
- [Prior Mismatch and Adaptation in PnP-ADMM with a Nonconvex Convergence Analysis](https://mlsanity.com/paper/2310.00133/) (2023)
- [Practical Phase Retrieval Using Double Deep Image Priors](https://mlsanity.com/paper/2211.00799/) (2022)
- [Deep Model-Based Architectures for Inverse Problems under Mismatched Priors](https://mlsanity.com/paper/2207.13200/) (2022)
- [Block Coordinate Plug-and-Play Methods for Blind Inverse Problems](https://mlsanity.com/paper/2305.12672/) (2023)
- [Plug-and-Play Posterior Sampling under Mismatched Measurement and Prior Models](https://mlsanity.com/paper/2310.03546/) (2023)
- [Non-Iterative Phase Retrieval With Cascaded Neural Networks](https://mlsanity.com/paper/2106.10195/) (2021)
- [Dynamic Proximal Unrolling Network for Compressive Imaging](https://mlsanity.com/paper/2107.11007/) (2021)
- [DOLPH: Diffusion Models for Phase Retrieval](https://mlsanity.com/paper/2211.00529/) (2022)
- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [Monotonically Convergent Regularization by Denoising](https://mlsanity.com/paper/2202.04961/) (2022)
- [Deep Iterative Phase Retrieval for Ptychography](https://mlsanity.com/paper/2202.10573/) (2022)
- [Complex-valued Retrievals From Noisy Images Using Diffusion Models](https://mlsanity.com/paper/2212.03235/) (2022)
- [PRISTA-Net: Deep Iterative Shrinkage Thresholding Network for Coded Diffraction Patterns Phase Retrieval](https://mlsanity.com/paper/2309.04171/) (2023)
- [Deep-learning real-time phase retrieval of imperfect diffraction patterns from X-ray free-electron lasers](https://mlsanity.com/paper/2409.15784/) (2024)
- [Plug-and-Play Half-Quadratic Splitting for Ptychography](https://mlsanity.com/paper/2412.02548/) (2024)
- [RED-PSM: Regularization by Denoising of Factorized Low Rank Models for Dynamic Imaging](https://mlsanity.com/paper/2304.03483/) (2023)
- [What is Wrong with End-to-End Learning for Phase Retrieval?](https://mlsanity.com/paper/2403.15448/) (2024)
- [DDRM-PR: Fourier Phase Retrieval using Denoising Diffusion Restoration Models](https://mlsanity.com/paper/2501.03030/) (2025)
- [RSR-NF: Neural Field Regularization by Static Restoration Priors for Dynamic Imaging](https://mlsanity.com/paper/2503.10015/) (2025)
- [Plug-and-Play Posterior Sampling for Blind Inverse Problems](https://mlsanity.com/paper/2505.22923/) (2025)
- [PR-DAD: Phase Retrieval Using Deep Auto-Decoders](https://mlsanity.com/paper/2204.09051/) (2022)
- [Optimizing Intermediate Representations of Generative Models for Phase Retrieval](https://mlsanity.com/paper/2205.15617/) (2022)

## Abstract (arXiv)

Phase retrieval algorithms have become an important component in many modern computational imaging systems. For instance, in the context of ptychography and speckle correlation imaging, they enable imaging past the diffraction limit and through scattering media, respectively. Unfortunately, traditional phase retrieval algorithms struggle in the presence of noise. Progress has been made recently on more robust algorithms using signal priors, but at the expense of limiting the range of supported measurement models (e.g., to Gaussian or coded diffraction patterns). In this work we leverage the regularization-by-denoising framework and a convolutional neural network denoiser to create prDeep, a new phase retrieval algorithm that is both robust and broadly applicable. We test and validate prDeep in simulation to demonstrate that it is robust to noise and can handle a variety of system models. A MatConvNet implementation of prDeep is available at https://github.com/ricedsp/prDeep.