  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.
