Accelerating ptychographic reconstructions using spectral initializations

Abstract

Ptychography is a promising phase retrieval technique for label-free quantitative phase imaging. Recent advances in phase retrieval algorithms witnessed the development of spectral methods to accelerate gradient descent algorithms. Using spectral initializations on experimental data, for the first time, we report three times faster ptychographic reconstructions than with a standard gradient descent algorithm and improved resilience to noise. Coming at no additional computational cost compared to gradient-descent-based algorithms, spectral methods have the potential to be implemented in large-scale iterative ptychographic algorithms.

Phase Retrieval: From Computational Imaging to Machine Learning: A tutorial

“…Importantly, the convergence toward the leading eigenvector is ensured, a guarantee that is missing in many other nonlinear optimization strategies. Unlike convex-relaxation methods, spectral methods do not involve a lifting process either, thus simplifying their adoption in imaging settings such as ptychography [34]. The solution estimated via spectral methods is then typically refined with an iterative optimization algorithm, such as gradient descent.…”

Phase retrieval algorithm for the reconstruction of scattered images for visible and X-ray light sources

“…From a mathematical perspective, the magnitude of the spatial Fourier spectrum of the object is derivable from its autocorrelation, though this process results in the loss of phase information. Fortunately, powerful phase retrieval algorithms (PRAs), such as Gerchberg–Saxton, 17 error reduction (ER), 18 hybrid input-output (HIO), 18 semi-definite programming, 19 algorithm based on the transport of intensity equation, 20 and spectral methods, 21 as well as the combined HIO-ER algorithm and others, effectively reconstruct the lost phase distribution. PRAs are iterative methods applied in both the spatial and Fourier domains, and they can employ priori information as constraints (e.g., real and nonnegative, 18 total variation, 6 and non-zero pixel (NNP) 22 constraints).…”