Phase Retrieval with One or Two Diffraction Patterns by Alternating Projection with Null Initialization

2015/10/26 by Pengwen Chen, Chen, Pengwen, Albert Fannjiang +3 · 2 citations
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Advanced Electron Microscopy Techniques and Applications #Advanced X-ray Imaging Techniques #Data Analysis #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Optics (physics.optics) #Statistics and Probability (physics.data-an) #X-ray Spectroscopy and Fluorescence Analysis

paper · pdf · doi:10.48550/arxiv.1510.07379

openalex publication_date 2015/10/26 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01

Abstract

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 for initial guess and proved to produce asymptotically accurate initialization for the case of Gaussian random measurement. Numerical experiments show that the null initialization produces more accurate initial guess than the spectral initialization and that AP converges faster to the true object than other iterative schemes for non-convex optimization such as the Wirtinger Flow. In numerical experiments, AP with the null initialization converges globally to the true object.

Citations

• Phase Retrieval with Application to Optical Imaging: A contemporary overview
• Saving phase: Injectivity and stability for phase retrieval
• Invertibility and Robustness of Phaseless Reconstruction
• PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming
• Phase Recovery, MaxCut and Complex Semidefinite Programming

Cited by

• PhaseLift for Coded Diffraction Patterns: Optimal Sampling Rate
• PhasePack User Guide

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