Stable Optimizationless Recovery from Phaseless Linear Measurements
Name
Demanet_Stable optimizationless.pdf
Size
216.3 KB
Format
Adobe PDF
Checksum (MD5)
cd4b18cee78f69442e36e3e168085ec0
Author(s)
Demanet, Laurent
Hand, Paul
Date Issued
November 2013
Journal
Journal of Fourier Analysis and Applications
Publisher
Springer-Verlag
Citation
Demanet, Laurent, and Paul Hand. “Stable Optimizationless Recovery from Phaseless Linear Measurements.” J Fourier Anal Appl 20, no. 1 (November 14, 2013): 199–221.
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s00041-013-9305-2
