Workshop on Phaseless Reconstruction

Paul Hand


Stable optimizationless recovery from random phaseless measurements


We address the problem of recovering an n-vector from m random, 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 is unnecessary. We further demonstrate that a simple algorithm of projection onto convex sets converges linearly toward the unique solution.