# Plug-and-Play Half-Quadratic Splitting for Ptychography

arXiv: https://arxiv.org/abs/2412.02548 · HTML: https://mlsanity.com/paper/2412.02548/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 41 references that are in the map.
- First posted on arXiv 3 Dec 2024.

## Builds on (most cited first, 7 of 7)

- [Diffusion models as plug-and-play priors](https://mlsanity.com/paper/2206.09012/) (2022)
- [Plug-and-Play Methods Provably Converge with Properly Trained Denoisers](https://mlsanity.com/paper/1905.05406/) (2019)
- [Gradient Step Denoiser for convergent Plug-and-Play](https://mlsanity.com/paper/2110.03220/) (2021)
- [PnP-Flow: Plug-and-Play Image Restoration with Flow Matching](https://mlsanity.com/paper/2410.02423/) (2024)
- [Proximal Denoiser for Convergent Plug-and-Play Optimization with Nonconvex Regularization](https://mlsanity.com/paper/2201.13256/) (2022)
- [prDeep: Robust Phase Retrieval with a Flexible Deep Network](https://mlsanity.com/paper/1803.00212/) (2018)
- [Fast and Robust Phase Retrieval via Deep Expectation-Consistent Approximation](https://mlsanity.com/paper/2407.09687/) (2024)

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

- [Position-Blind Ptychography: Viability of image reconstruction via data-driven variational inference](https://mlsanity.com/paper/2509.25269/) (2025)
- [Breaking the Weak Recovery Limit in Random Phase Retrieval with Learned Regularizers](https://mlsanity.com/paper/2509.15026/) (2025)
- [Machine Learning-Augmented Acceleration of Iterative Ptychographic Reconstruction](https://mlsanity.com/paper/2605.01122/) (2026)

## Abstract (arXiv)

Ptychography is a coherent diffraction imaging method that uses phase retrieval techniques to reconstruct complex-valued images. It achieves this by sequentially illuminating overlapping regions of a sample with a coherent beam and recording the diffraction pattern. Although this addresses traditional imaging system challenges, it is computationally intensive and highly sensitive to noise, especially with reduced illumination overlap. Data-driven regularisation techniques have been applied in phase retrieval to improve reconstruction quality. In particular, plug-and-play (PnP) offers flexibility by integrating data-driven denoisers as implicit priors. In this work, we propose a half-quadratic splitting framework for using PnP and other data-driven priors for ptychography. We evaluate our method both on natural images and real test objects to validate its effectiveness for ptychographic image reconstruction.