Gradient descent in phase retrieval

Abstract

Alternating projections, like Griffin-Lim and Fast Griffin-Lim algorithms, are among the most widely used iterative methods for phase retrieval. In this paper, we build upon the appendix of the original paper by Griffin and Lim and formulate them as gradient descent algorithms. By this approach, we can give convergence guarantees, evaluate the rate of convergence, and introduce a new phase recovery method based on the Nesterov acceleration of the gradient descent.