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.

翻译：从信号变换（如傅里叶变换）的幅度中恢复信号的过程被称为相位恢复问题，这在工程和应用物理的多个领域具有重要意义。本文提出了一种基于惯性/动量的快速相位恢复算法，并证明了该新算法以及快速Griffin-Lim算法的收敛性保证——后者在过去十年中其收敛性一直未得到证明。在最后一章中，我们将该算法应用于短时傅里叶变换相位恢复，并与Griffin-Lim算法、FGLA以及其他常用于此类问题的迭代算法进行了比较。