Year: 2016
Type: preprint
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 $|\langle a_i, x_0 \rangle | + η_i, \quad i =1,2\ldots m$ with high probability for $m = O(n)$, where $a_i \in \mathbb{R}^n$ are i.i.d standard Gaussian and $η\in \mathbb{R}^m$ 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.
Source: arXiv (Cornell University)
Authors: Hand, Paul, Voroninski, Vladislav
Institution: Rice University
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W2565234576