PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming

Details PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming

2011-09-21

arxiv.org/abs/1109.4499v1

Computer Science

Information Theory

Scientific paper

Suppose we wish to recover a signal x in C^n from m intensity measurements of the form ||^2, i = 1, 2,..., m; that is, from data in which phase information is missing. We prove that if the vectors z_i are sampled independently and uniformly at random on the unit sphere, then the signal x can be recovered exactly (up to a global phase factor) by solving a convenient semidefinite program---a trace-norm minimization problem; this holds with large probability provided that m is on the order of n log n, and without any assumption about the signal whatsoever. This novel result demonstrates that in some instances, the combinatorial phase retrieval problem can be solved by convex programming techniques. Finally, we also prove that our methodology is robust vis a vis additive noise.

Affiliated with

Also associated with

No associations

Rating

PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and PhaseLift: Exact and Stable Signal Recovery from Magnitude Measurements via Convex Programming will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-257146