A Closer Look at Reference Learning for Fourier Phase Retrieval

TL;DR

This paper investigates a modified phase retrieval problem involving reference images, analyzing an unrolled GS algorithm for learning references and proposing heuristics for constructing effective references, with promising results.

Contribution

It introduces a method to learn reference images for phase retrieval and proposes heuristics for constructing references without learning, enhancing reconstruction quality.

Findings

Learned references can improve phase retrieval accuracy.

Heuristic reference construction can match learned reference performance.

Analysis of unrolled GS algorithm for reference learning.

Abstract

Reconstructing images from their Fourier magnitude measurements is a problem that often arises in different research areas. This process is also referred to as phase retrieval. In this work, we consider a modified version of the phase retrieval problem, which allows for a reference image to be added onto the image before the Fourier magnitudes are measured. We analyze an unrolled Gerchberg-Saxton (GS) algorithm that can be used to learn a good reference image from a dataset. Furthermore, we take a closer look at the learned reference images and propose a simple and efficient heuristic to construct reference images that, in some cases, yields reconstructions of comparable quality as approaches that learn references. Our code is available at https://github.com/tuelwer/reference-learning.