# Solving Phase Retrieval with a Learned Reference

arXiv: https://arxiv.org/abs/2007.14621 · HTML: https://mlsanity.com/paper/2007.14621/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jul 2020.

## Built on by (most cited first, 8 of 8)

- [Phase Retrieval using Expectation Consistent Signal Recovery Algorithm based on Hypernetwork](https://mlsanity.com/paper/2101.04348/) (2021)
- [Realistic Defocus Blur for Multiplane Computer-Generated Holography](https://mlsanity.com/paper/2205.07030/) (2022)
- [Complex-valued Retrievals From Noisy Images Using Diffusion Models](https://mlsanity.com/paper/2212.03235/) (2022)
- [A Closer Look at Reference Learning for Fourier Phase Retrieval](https://mlsanity.com/paper/2110.13688/) (2021)
- [Optimizing Intermediate Representations of Generative Models for Phase Retrieval](https://mlsanity.com/paper/2205.15617/) (2022)
- [Low-light phase retrieval with implicit generative priors](https://mlsanity.com/paper/2402.17745/) (2024)
- [Untrained neural network embedded Fourier phase retrieval from few measurements](https://mlsanity.com/paper/2307.08717/) (2023)
- [Pupil Design for Computational Wavefront Estimation](https://mlsanity.com/paper/2604.00225/) (2026)

## Abstract (arXiv)

Fourier phase retrieval is a classical problem that deals with the recovery of an image from the amplitude measurements of its Fourier coefficients. Conventional methods solve this problem via iterative (alternating) minimization by leveraging some prior knowledge about the structure of the unknown image. The inherent ambiguities about shift and flip in the Fourier measurements make this problem especially difficult; and most of the existing methods use several random restarts with different permutations. In this paper, we assume that a known (learned) reference is added to the signal before capturing the Fourier amplitude measurements. Our method is inspired by the principle of adding a reference signal in holography. To recover the signal, we implement an iterative phase retrieval method as an unrolled network. Then we use back propagation to learn the reference that provides us the best reconstruction for a fixed number of phase retrieval iterations. We performed a number of simulations on a variety of datasets under different conditions and found that our proposed method for phase retrieval via unrolled network and learned reference provides near-perfect recovery at fixed (small) computational cost. We compared our method with standard Fourier phase retrieval methods and observed significant performance enhancement using the learned reference.