# Alternating Phase Langevin Sampling with Implicit Denoiser Priors for Phase Retrieval

arXiv: https://arxiv.org/abs/2211.00884 · HTML: https://mlsanity.com/paper/2211.00884/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 20 references that are in the map.
- First posted on arXiv 2 Nov 2022.

## Builds on (most cited first, 11 of 11)

- [Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising](https://mlsanity.com/paper/1608.03981/) (2016)
- [The Little Engine that Could: Regularization by Denoising (RED)](https://mlsanity.com/paper/1611.02862/) (2016)
- [Regularization by Denoising: Clarifications and New Interpretations](https://mlsanity.com/paper/1806.02296/) (2018)
- [Robust and interpretable blind image denoising via bias-free convolutional neural networks](https://mlsanity.com/paper/1906.05478/) (2019)
- [Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser](https://mlsanity.com/paper/2007.13640/) (2020)
- [Phase Retrieval Under a Generative Prior](https://mlsanity.com/paper/1807.04261/) (2018)
- [Phase Retrieval using Alternating Minimization](https://mlsanity.com/paper/1306.0160/) (2013)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [PhaseMax: Convex Phase Retrieval via Basis Pursuit](https://mlsanity.com/paper/1610.07531/) (2016)
- [Experimental robustness of Fourier Ptychography phase retrieval algorithms](https://mlsanity.com/paper/1511.02986/) (2015)
- [Sparse Phase Retrieval: Convex Algorithms and Limitations](https://mlsanity.com/paper/1303.4128/) (2013)

## Built on by (most cited first, 1 of 1)

- [GaiaFlow: Semantic-Guided Diffusion Tuning for Carbon-Frugal Search](https://mlsanity.com/paper/2602.15423/) (2026)

## Abstract (arXiv)

Phase retrieval is the nonlinear inverse problem of recovering a true signal from its Fourier magnitude measurements. It arises in many applications such as astronomical imaging, X-Ray crystallography, microscopy, and more. The problem is highly ill-posed due to the phase-induced ambiguities and the large number of possible images that can fit to the given measurements. Thus, there's a rich history of enforcing structural priors to improve solutions including sparsity priors and deep-learning-based generative models. However, such priors are often limited in their representational capacity or generalizability to slightly different distributions. Recent advancements in using denoisers as regularizers for non-convex optimization algorithms have shown promising performance and generalization. We present a way of leveraging the prior implicitly learned by a denoiser to solve phase retrieval problems by incorporating it in a classical alternating minimization framework. Compared to performant denoising-based algorithms for phase retrieval, we showcase competitive performance with Fourier measurements on in-distribution images and notable improvement on out-of-distribution images.