# Online Regularization by Denoising with Applications to Phase Retrieval

arXiv: https://arxiv.org/abs/1909.02040 · HTML: https://mlsanity.com/paper/1909.02040/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Sep 2019.

## Built on by (most cited first, 12 of 12)

- [Denoising: A Powerful Building-Block for Imaging, Inverse Problems, and Machine Learning](https://mlsanity.com/paper/2409.06219/) (2024)
- [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)
- [Taking a Big Step: Large Learning Rates in Denoising Score Matching Prevent Memorization](https://mlsanity.com/paper/2502.03435/) (2025)
- [Patch-Based Diffusion Models Beat Whole-Image Models for Mismatched Distribution Inverse Problems](https://mlsanity.com/paper/2410.11730/) (2024)
- [Non-Iterative Phase Retrieval With Cascaded Neural Networks](https://mlsanity.com/paper/2106.10195/) (2021)
- [DOLPH: Diffusion Models for Phase Retrieval](https://mlsanity.com/paper/2211.00529/) (2022)
- [Stochastic Generative Plug-and-Play Priors](https://mlsanity.com/paper/2604.03603/) (2026)
- [PR-DAD: Phase Retrieval Using Deep Auto-Decoders](https://mlsanity.com/paper/2204.09051/) (2022)
- [Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior](https://mlsanity.com/paper/2305.07712/) (2023)
- [Regularization by Neural Style Transfer for MRI Field-Transfer Reconstruction with Limited Data](https://mlsanity.com/paper/2308.10968/) (2023)

## Abstract (arXiv)

Regularization by denoising (RED) is a powerful framework for solving imaging inverse problems. Most RED algorithms are iterative batch procedures, which limits their applicability to very large datasets. In this paper, we address this limitation by introducing a novel online RED (On-RED) algorithm, which processes a small subset of the data at a time. We establish the theoretical convergence of On-RED in convex settings and empirically discuss its effectiveness in non-convex ones by illustrating its applicability to phase retrieval. Our results suggest that On-RED is an effective alternative to the traditional RED algorithms when dealing with large datasets.