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.
The following archive ltfatnote059.zip contains scripts and data for reproducing figures and tables from the paper. An extended summary of tested parameter combinations can, along with their resulting SNR, be downloaded from here.
Please note that LTFAT toolbox (version>=2.5.0 or the current development version, available here) and the PHASERET toolbox (current development version, available here) must be installed in order to run the scripts and reproduce the data.