# Corruption Robust Phase Retrieval via Linear Programming

arXiv: https://arxiv.org/abs/1612.03547 · HTML: https://mlsanity.com/paper/1612.03547/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2016.

## Built on by (most cited first, 1 of 1)

- [Tractable Gaussian Phase Retrieval with Heavy Tails and Adversarial Corruption with Near-Linear Sample Complexity](https://mlsanity.com/paper/2601.18245/) (2026)

## Abstract (arXiv)

We consider the problem of phase retrieval from corrupted magnitude observations. In particular we show that a fixed x0 ∈ ℝn can be recovered exactly from corrupted magnitude measurements |langle ai, x0 rangle | + ηi, quad i =1,2ldots m with high probability for m = O(n), where ai ∈ ℝn are i.i.d standard Gaussian and η ∈ ℝm 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.