A Closer Look at Reference Learning for Fourier Phase Retrieval

Tobias Uelwer, Nick Rucks, Stefan Harmeling

Keywords: Fourier phase retrieval, algorithm unrolling, reference image, Gerchberg-Saxton algorithm

TL;DR: We show how the Gerchberg-Saxton algorithm can be unrolled to learn a reference for Fourier phase retrieval and we analyze the performance gain of learned references over references that were not learned.

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.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2110.13688/code)