October 16, 2017
In our recent paper, we present an exact asymptotic analysis of the PhaseMax method for solving the phase retrieval problem via linear programming. Our analysis reveals a sharp phase transition phenomenon, and it also verifies our previous predictions made by the non-rigorous replica method from statistical physics. In addition, we propose a new iterative algorithm, named PhaseLamp, based on the idea of successive linearization and maximization over a polytope. This new algorithm has provably superior recovery performance over the original PhaseMax method.