Phase Retrieval by the Inverse Power Method

Phase retrieval is to recover signals from phaseless linear measurements. The most efficient methods to tackle this problem are nonconvex gradient approaches, which however generally need an elaborate initialized guess to ensure successful reconstruction. The inverse power method is proposed to provide a more accurate initialization. Numerical experiments illustrate the higher accuracy of the proposed method over other initialization methods. And we further demonstrate the iterative use of the initialization method can obtain an even better estimate.