Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns
Information Theory
2012-09-18 v2 math.IT
Numerical Analysis
Abstract
This note shows that we can recover a complex vector x in C^n exactly from on the order of n quadratic equations of the form |<a_i, x>|^2 = b_i, i = 1, ..., m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in [3], which required the number of equations to be at least on the order of n log n. We also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results.
Cite
@article{arxiv.1208.6247,
title = {Solving Quadratic Equations via PhaseLift when There Are About As Many Equations As Unknowns},
author = {Emmanuel J. Candes and Xiaodong Li},
journal= {arXiv preprint arXiv:1208.6247},
year = {2012}
}
Comments
6 pages