Journal
FOUNDATIONS OF COMPUTATIONAL MATHEMATICS
Volume 14, Issue 5, Pages 1017-1026Publisher
SPRINGER
DOI: 10.1007/s10208-013-9162-z
Keywords
Phase retrieval; PhaseLift; Semidefinite relaxations of nonconvex quadratic programs; Deviation inequalities for random matrices
Funding
- AFOSR [FA9550-09-1-0643]
- ONR [N00014-09-1-0258]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [0963835] Funding Source: National Science Foundation
Ask authors/readers for more resources
This note shows that we can recover any complex vector exactly from on the order of n quadratic equations of the form |aOE (c) a (i) ,x (0)>|(2)=b (i) , i=1,aEuro broken vertical bar,m, by using a semidefinite program known as PhaseLift. This improves upon earlier bounds in CandSs et al. (Commun. Pure Appl. Math. 66:1241-1274, 2013), which required the number of equations to be at least on the order of nlogn. Further, we show that exact recovery holds for all input vectors simultaneously, and also demonstrate optimal recovery results from noisy quadratic measurements; these results are much sharper than previously known results.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available
Share Paper
