# Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation

arXiv: https://arxiv.org/abs/2407.09687 · HTML: https://mlsanity.com/paper/2407.09687/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 87 references that are in the map.
- First posted on arXiv 12 Jul 2024.

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

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [Deep Image Prior](https://mlsanity.com/paper/1711.10925/) (2017)
- [Compressed Sensing using Generative Models](https://mlsanity.com/paper/1703.03208/) (2017)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Phase Retrieval via Wirtinger Flow: Theory and Algorithms](https://mlsanity.com/paper/1407.1065/) (2014)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Principled Probabilistic Imaging using Diffusion Models as Plug-and-Play Priors](https://mlsanity.com/paper/2405.18782/) (2024)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Provably Robust Score-Based Diffusion Posterior Sampling for Plug-and-Play Image Reconstruction](https://mlsanity.com/paper/2403.17042/) (2024)
- [Phase recovery and holographic image reconstruction using deep learning in neural networks](https://mlsanity.com/paper/1705.04286/) (2017)
- [Lensless computational imaging through deep learning](https://mlsanity.com/paper/1702.08516/) (2017)
- [Fundamental Limits of Weak Recovery with Applications to Phase Retrieval](https://mlsanity.com/paper/1708.05932/) (2017)
- [Phase retrieval in high dimensions: Statistical and computational phase transitions](https://mlsanity.com/paper/2006.05228/) (2020)
- [Phase Retrieval from Coded Diffraction Patterns](https://mlsanity.com/paper/1310.3240/) (2013)
- [PhaseMax: Convex Phase Retrieval via Basis Pursuit](https://mlsanity.com/paper/1610.07531/) (2016)
- [Deep Phase Decoder: Self-calibrating phase microscopy with an untrained deep neural network](https://mlsanity.com/paper/2001.09803/) (2020)
- [Approximate Message Passing with Spectral Initialization for Generalized Linear Models](https://mlsanity.com/paper/2010.03460/) (2020)
- [The Numerics of Phase Retrieval](https://mlsanity.com/paper/2004.05788/) (2020)
- [Inference with Deep Generative Priors in High Dimensions](https://mlsanity.com/paper/1911.03409/) (2019)
- [Experimental robustness of Fourier Ptychography phase retrieval algorithms](https://mlsanity.com/paper/1511.02986/) (2015)
- [Expectation Consistent Approximate Inference: Generalizations and Convergence](https://mlsanity.com/paper/1602.07795/) (2016)
- [When deep denoising meets iterative phase retrieval](https://mlsanity.com/paper/2003.01792/) (2020)
- [D-VDAMP: Denoising-based Approximate Message Passing for Compressive MRI](https://mlsanity.com/paper/2010.13211/) (2020)
- [Complex-valued Retrievals From Noisy Images Using Diffusion Models](https://mlsanity.com/paper/2212.03235/) (2022)
- [Denoising Generalized Expectation-Consistent Approximation for MR Image Recovery](https://mlsanity.com/paper/2206.05049/) (2022)

## Built on by (most cited first, 2 of 2)

- [Plug-and-Play Half-Quadratic Splitting for Ptychography](https://mlsanity.com/paper/2412.02548/) (2024)
- [prNet: Data-Driven Phase Retrieval via Stochastic Refinement](https://mlsanity.com/paper/2507.09608/) (2025)

## Abstract (arXiv)

Accurately recovering images from phaseless measurements is a challenging and long-standing problem. In this work, we present "deepECpr," which combines expectation-consistent (EC) approximation with deep denoising networks to surpass state-of-the-art phase-retrieval methods in both speed and accuracy. In addition to applying EC in a non-traditional manner, deepECpr includes a novel stochastic damping scheme that is inspired by recent diffusion methods. Like existing phase-retrieval methods based on plug-and-play priors, regularization by denoising, or diffusion, deepECpr iterates a denoising stage with a measurement-exploitation stage. But unlike existing methods, deepECpr requires far fewer denoiser calls. We compare deepECpr to the state-of-the-art prDeep (Metzler et al., 2018), Deep-ITA (Wang et al., 2020), DOLPH (Shoushtari et al., 2023), and Diffusion Posterior Sampling (Chung et al., 2023) methods for noisy phase-retrieval of color, natural, and unnatural grayscale images on oversampled-Fourier and coded-diffraction-pattern measurements and find improvements in both PSNR and SSIM with significantly fewer denoiser calls.