A direct solver for the phase retrieval problem in ptychographic imaging

TL;DR

This paper introduces a generalized direct solver for the phase retrieval problem in ptychographic imaging, improving stability especially with missing data, based on extensions of previous Fourier-based methods.

Contribution

It extends existing phase retrieval algorithms to better handle ptychographic data and demonstrates enhanced stability through numerical experiments.

Findings

The new method is more stable than previous algorithms.

It performs well even with missing data.

Numerical experiments confirm improved robustness.

Abstract

Measurements achieved with ptychographic imaging are a special case of diffraction measurements. They are generated by illuminating small parts of a sample with, e.g., a focused X-ray beam. By shifting the sample, a set of far-field diffraction patterns of the whole sample are then obtained. From a mathematical point of view those measurements are the squared modulus of the windowed Fourier transform of the sample. Thus, we have a phase retrieval problem for local Fourier measurements. A direct solver for this problem was introduced by Iwen, Viswanathan and Wang in 2016 and improved by Iwen, Preskitt, Saab and Viswanathan in 2018. Motivated by the applied perspective of ptychographic imaging, we present a generalization of this method and compare the different versions in numerical experiments. The new method proposed herein turns out to be more stable, particularly in the case of missing data.