Accelerated Wirtinger Flow: A fast algorithm for ptychography

TL;DR

The paper introduces Accelerated Wirtinger Flow, a fast, robust algorithm for ptychographic image reconstruction that converges quickly without manual parameter tuning, outperforming classical methods in speed and image quality.

Contribution

It combines Nesterov's acceleration with Wirtinger gradient descent, providing a parameter-free, efficient algorithm for ptychography reconstruction.

Findings

Fast convergence demonstrated in simulated X-ray ptychography

Achieves higher image quality with less computation

Robust to noise and probe misalignment

Abstract

This paper presents a new algorithm, Accelerated Wirtinger Flow (AWF), for ptychographic image reconstruction from phaseless diffraction pattern measurements. AWF is based on combining Nesterov's acceleration approach with Wirtinger gradient descent. Theoretical results enable prespecification of all AWF algorithm parameters, with no need for computationally-expensive line searches and no need for manual parameter tuning. AWF is evaluated in the context of simulated X-ray ptychography, where we demonstrate fast convergence and low per-iteration computational complexity. We also show examples where AWF reaches higher image quality with less computation than classical algorithms. AWF is also shown to have robustness to noise and probe misalignment.