# Accelerated Wirtinger Flow: A fast algorithm for ptychography

arXiv: https://arxiv.org/abs/1806.05546 · HTML: https://mlsanity.com/paper/1806.05546/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2018.

## Built on by (most cited first, 5 of 5)

- [PtychoDV: Vision Transformer-Based Deep Unrolling Network for Ptychographic Image Reconstruction](https://mlsanity.com/paper/2310.07504/) (2023)
- [Ptychographic Image Reconstruction from Limited Data via Score-Based Diffusion Models with Physics-Guidance](https://mlsanity.com/paper/2502.18767/) (2025)
- [Poisson-Gaussian Holographic Phase Retrieval with Score-based Image Prior](https://mlsanity.com/paper/2305.07712/) (2023)
- [Acceleration and Implicit Regularization in Gaussian Phase Retrieval](https://mlsanity.com/paper/2311.12888/) (2023)
- [Physics-Guided Diffusion Priors for Multi-Slice Reconstruction in Scientific Imaging](https://mlsanity.com/paper/2512.06977/) (2025)

## Abstract (arXiv)

This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger gradient descent. Theoretical results enable prespecification of all AWF algorithm parameters, with no need for computationally-expensive line searches and no need for manual parameter tuning. AWF is evaluated in the context of simulated X-ray ptychography, where we demonstrate fast convergence and low per-iteration computational complexity. We also show examples where AWF reaches higher image quality with less computation than classical algorithms. AWF is also shown to have robustness to noise and probe misalignment.