Fast angular synchronization for phase retrieval via incomplete information

Aditya Viswanathan; Mark Iwen

doi:10.1117/12.2186336

24 August 2015 Fast angular synchronization for phase retrieval via incomplete information

Aditya Viswanathan, Mark Iwen

Proceedings Volume 9597, Wavelets and Sparsity XVI; 959718 (2015) https://doi.org/10.1117/12.2186336
Event: SPIE Optical Engineering + Applications, 2015, San Diego, California, United States

Abstract

We consider the problem of recovering the phase of an unknown vector, x ∈ ℂ^d, given (normalized) phase difference measurements of the form x_jx_k^*/|x_jx_k^*|, j,k ∈ {1,...,d}, and where x_j^* denotes the complex conjugate of x_j. 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.

Citation Download Citation

Aditya Viswanathan and Mark Iwen "Fast angular synchronization for phase retrieval via incomplete information", Proc. SPIE 9597, Wavelets and Sparsity XVI, 959718 (24 August 2015); https://doi.org/10.1117/12.2186336

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available