@article{b10fdec44bd54555ae7597d22201ebd3,
title = "Alternating projection, ptychographic imaging and phase synchronization",
abstract = "We demonstrate necessary and sufficient conditions of the local convergence of the alternating projection algorithm to a unique solution up to a global phase factor. Additionally, for the ptychography imaging problem, we discuss phase synchronization and graph connection Laplacian, and show how to construct an accurate initial guess to accelerate convergence speed to handle the big imaging data in the coming new light source era.",
keywords = "Alternating projection, Graph connection Laplacian, Phase retrieval, Phase synchronization, Ptychography",
author = "Stefano Marchesini and Tu, {Yu Chao} and Wu, {Hau Tieng}",
note = "Funding Information: This research was supported in part by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy , under contract DE-AC02-05CH11231 (SM) and by AFOSR grant FA9550-09-1-0643 (HT). The authors would like to thank Professor Arthur Szlam, Dr. Jeffrey J. Donatelli and Dr. Wenjing Liao for their inputs to improve the paper. H.-T. Wu thanks Professor Ingrid Daubechies and Professor Albert Fannajing for the discussion. We acknowledge NVIDIA for providing us with a Tesla K40 GPU for our tests. Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",
year = "2016",
month = nov,
day = "1",
doi = "10.1016/j.acha.2015.06.005",
language = "English (US)",
volume = "41",
pages = "815--851",
journal = "Applied and Computational Harmonic Analysis",
issn = "1063-5203",
publisher = "Academic Press Inc.",
number = "3",
}