Phase Retrieval via a Modified Null Vector Estimator

In the phase retrieval problem, an unknown vector or image is to be recovered from phaseless measurements. This paper puts forth a new initialization estimator called T-modified Null Initialization (TNI) for non-convex phase retrieval problem. The proposed TNI method provide accurate and stable initialization for phase retrieval with the information-theoretic limit number of samples. Its average relative error exponentially reduces as the oversampling ratio m/n grows, which can improve the performance of existing hybrid optimization method of phase retrieval. Experimental results clearly demonstrate the superiority of our proposed TNI estimator, which not only achieves a lower relative error of initialization but also outperforms the traditional methods in terms of accuracy and noise stability when measurements contaminated with noise.