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Proceedings Paper

Fast angular synchronization for phase retrieval via incomplete information
Author(s): Aditya Viswanathan; Mark Iwen
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Paper Abstract

We consider the problem of recovering the phase of an unknown vector, x ∈ ℂd, given (normalized) phase difference measurements of the form xjxk*/|xjxk*|, j,k ∈ {1,...,d}, and where xj* denotes the complex conjugate of xj. This problem is sometimes referred to as the angular synchronization problem. This paper analyzes a linear-time-in-d eigenvector-based angular synchronization algorithm and studies its theoretical and numerical performance when applied to a particular class of highly incomplete and possibly noisy phase difference measurements. Theoretical results are provided for perfect (noiseless) measurements, while numerical simulations demonstrate the robustness of the method to measurement noise. Finally, we show that this angular synchronization problem and the specific form of incomplete phase difference measurements considered arise in the phase retrieval problem - where we recover an unknown complex vector from phaseless (or magnitude) measurements.

Paper Details

Date Published: 24 August 2015
PDF: 8 pages
Proc. SPIE 9597, Wavelets and Sparsity XVI, 959718 (24 August 2015); doi: 10.1117/12.2186336
Show Author Affiliations
Aditya Viswanathan, Michigan State Univ. (United States)
Mark Iwen, Michigan State Univ. (United States)

Published in SPIE Proceedings Vol. 9597:
Wavelets and Sparsity XVI
Manos Papadakis; Vivek K. Goyal; Dimitri Van De Ville, Editor(s)

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