# Deep Plug-and-Play HIO Approach for Phase Retrieval

arXiv: https://arxiv.org/abs/2411.18967 · HTML: https://mlsanity.com/paper/2411.18967/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Nov 2024.

## Built on by (most cited first, 3 of 3)

- [prNet: Data-Driven Phase Retrieval via Stochastic Refinement](https://mlsanity.com/paper/2507.09608/) (2025)
- [I2I-PR: Deep Iterative Refinement for Phase Retrieval using Image-to-Image Diffusion Models](https://mlsanity.com/paper/2507.09609/) (2025)
- [Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizers](https://mlsanity.com/paper/2509.15026/) (2025)

## Abstract (arXiv)

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear and ill-posed nature. Recently, learning-based approaches have emerged as powerful alternatives to the analytical methods for several inverse problems. In the context of phase retrieval, a novel plug-and-play approach that exploits learning-based prior and efficient update steps has been presented at the Computational Optical Sensing and Imaging topical meeting, with demonstrated state-of-the-art performance. The key idea was to incorporate learning-based prior to the Gerchberg-Saxton type algorithms through plug-and-play regularization. In this paper, we present the mathematical development of the method including the derivation of its analytical update steps based on half-quadratic splitting and comparatively evaluate its performance through extensive simulations on a large test dataset. The results show the effectiveness of the method in terms of both image quality, computational efficiency, and robustness to initialization and noise.