  Phase retrieval is a problem encountered not only in speech and audio
processing, but in many other fields such as optics. Iterative algorithms based
on non-convex set projections are effective and frequently used for retrieving
the phase when only STFT magnitudes are available. While the basic Griffin-Lim
algorithm and its variants have been the prevalent method for decades, more
recent advances, e.g. in optics, raise the question: Can we do better than
Griffin-Lim for speech signals, using the same principle of iterative
projection?
  In this paper we compare the classical algorithms in the speech domain with
two modern methods from optics with respect to reconstruction quality and
convergence rate. Based on this study, we propose to combine Griffin-Lim with
the Difference Map algorithm in a hybrid approach which shows superior results,
in terms of both convergence and quality of the final reconstruction.
