Weighted Null Vector Initialization and its Application to Phase Retrieval

Abstract

Phase retrieval problem is an nonlinear inverse problem of recovering real- or complex-valued signal from quadratic measurements, which arises in various applications. The best-known algorithms for solving this problem are non-convex methods starting with spectral initializers that provide an initial point within a local basin sufficiently close to the target signal. This paper introduces a simple method, called weighted null vector initialization (WNI), which can be used to compute accurate initialization vectors for solving non-convex phase retrieval. The introduced WNI method is more robust against measurement noise and outperforms the best spectral initializer, and null initializer. Simulation results are provided to illustrate the effectiveness of the proposed method.