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標題: Fourier phase retrieval with a single mask by Douglas-Rachford algorithms
作者: Chen, Pengwen
Fannjiang, Albert
關鍵字: Douglas-Rachford algorithm;Phase retrieval;coded diffraction pattern;geometric convergence;spectral gap
Project: Applied and computational harmonic analysis, Volume 44, Issue 3, Page(s) 665-699.
The Fourier-domain Douglas-Rachford (FDR) algorithm is analyzed for phase retrieval with a single random mask. Since the uniqueness of phase retrieval solution requires more than a single oversampled coded diffraction pattern, the extra information is imposed in either of the following forms: 1) the sector condition on the object; 2) another oversampled diffraction pattern, coded or uncoded. For both settings, the uniqueness of projected fixed point is proved and for setting 2) the local, geometric convergence is derived with a rate given by a spectral gap condition. Numerical experiments demonstrate global, power-law convergence of FDR from arbitrary initialization for both settings as well as for 3 or more coded diffraction patterns without oversampling. In practice, the geometric convergence can be recovered from the power-law regime by a simple projection trick, resulting in highly accurate reconstruction from generic initialization.
ISSN: 1063-5203
DOI: 10.1016/j.acha.2016.07.003
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