Stable optimizationless recovery from phaseless linear measurements

Paul Hand


We will discuss the problem of recovering an n-vector from m linear measurements lacking sign or phase information. We will use the technique of lifting to pose a semidefinite relaxation of the problem. In this setting, the n-vector can be recovered with high probability if m = O(n log n). The recovery method is optimizationless in the sense that trace minimization is unnecessary. We further demonstrate that the algorithm of projection onto convex sets converges linearly toward the unique solution.

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