Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/99123
標題: Phase Retrieval with One or Two Diffraction Patterns by Alternating Projections with the Null Initialization
作者: Pengwen Chen
Albert Fannjiang
Gi-Ren Liu
陳鵬文
關鍵字: Phase retrieval;Alternating projections;Local convergence;Spectral gap;Null initialization
出版社: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
Project: Journal of Fourier Analysis and Applications, Volume 24, Issue 3, pp 719–758
摘要: 
Alternating projection (AP) of various forms, including the parallel AP (PAP), real-constrained AP (RAP) and the serial AP (SAP), are proposed to solve phase retrieval with at most two coded diffraction patterns. The proofs of geometric convergence are given with sharp bounds on the rates of convergence in terms of a spectral gap condition. To compensate for the local nature of convergence, the null initialization is proposed to produce good-quality initial guess. Numerical experiments show that the null initialization is more accurate than the spectral initialization and that AP converges faster to the true object than other iterative schemes such as the Wirtinger flow (WF). In numerical experiments AP with the null initialization converges globally to the true object.
URI: http://hdl.handle.net/11455/99123
DOI: 10.1007/s00041-017-9536-8
Appears in Collections:應用數學系所

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