Gradient Methods in the Minimization of Quartic Functionals: Phase Retrieval in Circular Case

In this paper we investigate different optimization techniques to address phase retrieval by quartic functional minimization. In particular, in the first part of the paper we provide an estimation of the computational effort for gradient descent method and two different versions of non-linear conjugate gradient method (Fletcher-Reeves, and Polak-Ribière-Polyak). In the second part of the paper, with regard to the problem of reconstructing the field radiated by a source from phaseless measurements, we compare the considered optimization methods in terms of speed of convergence and accuracy on the reconstruction.