Stable Optimizationless Recovery from Phaseless Linear Measurements
Author(s)Demanet, Laurent; Hand, Paul
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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.
DepartmentMassachusetts Institute of Technology. Department of Mathematics
Journal of Fourier Analysis and Applications
Demanet, Laurent, and Paul Hand. “Stable Optimizationless Recovery from Phaseless Linear Measurements.” J Fourier Anal Appl 20, no. 1 (November 14, 2013): 199–221.
Author's final manuscript