Wirtinger Flow Method With Optimal Stepsize for Phase Retrieval

The recently reported Wirtinger flow (WF) algorithm has been demonstrated as a promising method for solving the problem of phase retrieval by applying a gradient descent scheme. An empirical choice of stepsize is suggested in practice. However, this heuristic stepsize selection rule is not optimal. In order to accelerate the convergence rate, we propose an improved WF with optimal stepsize. It is revealed that this optimal stepsize is the solution of a univariate cubic equation with real-valued coefficients. Finding its roots is computationally simple because a closed-form expression exists. Furthermore, compared with obtaining the coefficients of the cubic equation, calculating the gradient is still the leading cost. Therefore, the proposed approach has the same dominant cost as WF in each iteration. Simulation results are provided to validate its efficiency compared to the existing technique.