  The recovery of a signal from the magnitudes of its transformation, like the
Fourier transform, is known as the phase retrieval problem and is of big
relevance in various fields of engineering and applied physics. In this paper,
we present a fast inertial/momentum based algorithm for the phase retrieval
problem and we prove a convergence guarantee for the new algorithm and for the
Fast Griffin-Lim algorithm, whose convergence remained unproven in the past
decade. In the final chapter, we compare the algorithm for the Short Time
Fourier transform phase retrieval with the Griffin-Lim algorithm and FGLA and
to other iterative algorithms typically used for this type of problem.
