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arXiv · 1612.03547

Corruption Robust Phase Retrieval via Linear Programming

Paul Hand·Vladislav Voroninski
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Abstract

We consider the problem of phase retrieval from corrupted magnitude observations. In particular we show that a fixed $x_0 \in \mathbb{R}^n$ can be recovered exactly from corrupted magnitude measurements $|\langle a_i, x_0 \rangle | + \eta_i, \quad i =1,2\ldots m$ with high probability for $m = O(n)$, where $a_i \in \mathbb{R}^n$ are i.i.d standard Gaussian and $\eta \in \mathbb{R}^m$ has fixed sparse support and is otherwise arbitrary, by using a version of the PhaseMax algorithm augmented with slack variables subject to a penalty. This linear programming formulation, which we call RobustPhaseMax, operates in the natural parameter space, and our proofs rely on a direct analysis of the optimality conditions using concentration inequalities.

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Paul Hand, Vladislav Voroninski. 2016-12-12. Corruption Robust Phase Retrieval via Linear Programming. https://arxiv.org/abs/1612.03547

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