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

Accelerated Wirtinger Flow: A fast algorithm for ptychography