# A Geometric Analysis of Phase Retrieval

@article{Sun2016AGA,
title={A Geometric Analysis of Phase Retrieval},
author={Ju Sun and Qing Qu and John Wright},
journal={Foundations of Computational Mathematics},
year={2016},
volume={18},
pages={1131-1198}
}
• Published 22 February 2016
• Computer Science
• Foundations of Computational Mathematics
Can we recover a complex signal from its Fourier magnitudes? More generally, given a set of m measurements, $$y_k = \left| \varvec{a}_k^* \varvec{x} \right|$$yk=ak∗x for $$k = 1, \ldots , m$$k=1,…,m, is it possible to recover $$\varvec{x} \in \mathbb C^n$$x∈Cn (i.e., length-n complex vector)? This generalized phase retrieval (GPR) problem is a fundamental task in various disciplines and has been the subject of much recent investigation. Natural nonconvex heuristics often work remarkably well…
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