Ptychographic phase retrieval by proximal algorithms

• Published in: New journal of physics Vol. 22; no. 2; pp. 23035 - 23048
• Main Author: Yan, Hanfei
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.02.2020
• Subjects: Algorithms; Computational geometry; Computer simulation; Convergence; Convexity; Datasets; Gold; Iterative methods; MATERIALS SCIENCE; maximum-likelihood; Nanoparticles; Optimization; Phase retrieval; Physics; proximal algorithms; ptychographic phase-retrieval; x-ray imaging
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/ab704e

We derive a set of ptychography phase-retrieval iterative engines based on proximal algorithms originally developed in convex optimization theory, and discuss their connections with existing ones. The use of proximal operator creates a simple frame work that allows us to incorporate the effect of noise from a maximum-likelihood (ML) principle. We focus on three particular algorithms, namely proximal minimization, alternating direction method of multiplier and accelerated proximal gradient (APG). We benchmark their performance with numerical simulations, and discuss their optimal conditions for convergence and accuracy. An experimental dataset is used to demonstrate their effectiveness as well, in which case an array of cubic Au nanoparticles with a size of 50 nm is imaged. We show that with the presence of Poisson noise, a dataset with photon counts up to 104 at one detector pixel already requires ML-based methods to achieve a stable convergence. Among the three algorithms derived in this work, APG method is reported first time for its application in ptychographic reconstruction and shows superior performance in terms of both accuracy and convergence rate with a noisy dataset.