# Alternating Projection, Ptychographic Imaging and Phase Synchronization

arXiv: https://arxiv.org/abs/1402.0550 · HTML: https://mlsanity.com/paper/1402.0550/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2014.

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

- [Stochastic Light Field Holography](https://mlsanity.com/paper/2307.06277/) (2023)
- [A modular software framework for the design and implementation of ptychography algorithms](https://mlsanity.com/paper/2205.04295/) (2022)
- [Unrolled algorithms for group synchronization](https://mlsanity.com/paper/2207.09418/) (2022)
- [Optimal spectral initializers impact on phase retrieval phase transitions -- an RDT view](https://mlsanity.com/paper/2506.18279/) (2025)
- [Accelerate Vector Diffusion Maps by Landmarks](https://mlsanity.com/paper/2603.21247/) (2026)

## Abstract (arXiv)

We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychography imaging problem, we discuss phase synchronization and graph connection Laplacian, and show how to construct an accurate initial guess to accelerate convergence speed to handle the big imaging data in the coming new light source era.