Stable Optimizationless Recovery from Phaseless Linear Measurements
We address the problem of recovering an n-vector from m linear measurements lacking sign or phase information. We show that lifting and semidefinite relaxation suffice by themselves for stable recovery in the setting of m=O(nlogn) random sensing vectors, with high probability. The recovery method is...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Springer-Verlag,
2015-01-15T20:11:19Z.
|
| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | We address the problem of recovering an n-vector from m linear measurements lacking sign or phase information. We show that lifting and semidefinite relaxation suffice by themselves for stable recovery in the setting of m=O(nlogn) random sensing vectors, with high probability. The recovery method is optimizationless in the sense that trace minimization in the PhaseLift procedure is unnecessary. That is, PhaseLift reduces to a feasibility problem. The optimizationless perspective allows for a Douglas-Rachford numerical algorithm that is unavailable for PhaseLift. This method exhibits linear convergence with a favorable convergence rate and without any parameter tuning. National Science Foundation (U.S.) Alfred P. Sloan Foundation United States. Air Force Office of Scientific Research TOTAL (Firm) |
|---|