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arXiv · 1208.1803

Stable optimizationless recovery from phaseless linear measurements

Laurent Demanet·Paul Hand
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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(n log n) 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.

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Laurent Demanet, Paul Hand. 2012-08-09. Stable optimizationless recovery from phaseless linear measurements. https://arxiv.org/abs/1208.1803

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