Robust Initialization Estimator and its Application in Solving Quadratic Equations

Abstract

In many non-convex optimization-based signal recovery tasks, a good initial point is essential for the performance of the optimization process. One seeks to start the point from a small local region surrounding the targeted signal. Then an efficient iterative refinement procedure can help recover the wanted signal. Motivated by this fact, we introduce two efficient and robust estimators to find reasonably good initial points for non-convex phase retrieval algorithms. The proposed estimators can provide high quality initial guesses for phase retrieval even with a number of samples that is close to the information-theoretic limit. The average relative error reduces exponentially as the oversampling ratio grows, which can improve the performance of existing non-convex optimization methods. The experimental results clearly demonstrate the superiority of two introduced estimators, which not only obtain a more accurate estimate of the true solution but also outperform the existing methods in terms of noise robustness when measurements are contaminated with noise.