Study of cost functionals for ptychographic phase retrieval to improve the robustness against noise, and a proposal for another noise-robust ptychographic phase retrieval scheme

TL;DR

This paper investigates various cost functionals for ptychographic phase retrieval, highlighting the importance of step size reduction for noise robustness and proposing a new method that adapts intensity constraints to enhance reconstruction quality under noisy conditions.

Contribution

It compares different cost functionals for noise robustness and introduces a novel ptychographic reconstruction scheme based on adapting intensity constraints.

Findings

Reducing step size improves noise robustness in reconstructions.

Cost functionals based on maximum-likelihood approaches show consistent reliability.

The proposed method enhances reconstruction quality in noisy environments.

Abstract

Recently, efforts have been made to improve ptychography phase retrieval algorithms so that they are more robust against noise. Often the algorithm is adapted by changing the cost functional that needs to be minimized. In particular, it has been suggested that the cost functional should be obtained using a maximum-likelihood approach that takes the noise statistics into account. Here, we consider the different choices of cost functional, and to how they affect the reconstruction results. We find that seemingly the only consistently reliable way to improve reconstruction results in the presence of noise is to reduce the step size of the update function. In addition, a noise-robust ptychographic reconstruction method has been proposed that relies on adapting the intensity constraints