# Phase retrieval for Fourier Ptychography under varying amount of measurements

arXiv: https://arxiv.org/abs/1805.03593 · HTML: https://mlsanity.com/paper/1805.03593/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2018.

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

- [On the use of deep learning for phase recovery](https://mlsanity.com/paper/2308.00942/) (2023)
- [LWGNet: Learned Wirtinger Gradients for Fourier Ptychographic Phase Retrieval](https://mlsanity.com/paper/2208.04283/) (2022)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)
- [Deep learning phase recovery: data-driven, physics-driven, or combining both?](https://mlsanity.com/paper/2404.01360/) (2024)
- [Self-supervised physics-informed generative networks for phase retrieval from a single X-ray hologram](https://mlsanity.com/paper/2508.15530/) (2025)

## Abstract (arXiv)

Fourier Ptychography is a recently proposed imaging technique that yields high-resolution images by computationally transcending the diffraction blur of an optical system. At the crux of this method is the phase retrieval algorithm, which is used for computationally stitching together low-resolution images taken under varying illumination angles of a coherent light source. However, the traditional iterative phase retrieval technique relies heavily on the initialization and also need a good amount of overlap in the Fourier domain for the successively captured low-resolution images, thus increasing the acquisition time and data. We show that an auto-encoder based architecture can be adaptively trained for phase retrieval under both low overlap, where traditional techniques completely fail, and at higher levels of overlap. For the low overlap case we show that a supervised deep learning technique using an autoencoder generator is a good choice for solving the Fourier ptychography problem. And for the high overlap case, we show that optimizing the generator for reducing the forward model error is an appropriate choice. Using simulations for the challenging case of uncorrelated phase and amplitude, we show that our method outperforms many of the previously proposed Fourier ptychography phase retrieval techniques.