Accelerated Griffin-Lim algorithm: A fast and provably converging numerical method for phase retrieval

TL;DR

This paper introduces a new fast and provably convergent algorithm for phase retrieval, improving upon existing methods like Griffin-Lim and FGLA, with demonstrated efficiency in Fourier transform applications.

Contribution

The paper proposes an inertial/momentum-based phase retrieval algorithm with proven convergence, addressing a longstanding open problem for the Fast Griffin-Lim algorithm.

Findings

The new algorithm converges faster than traditional methods.

It outperforms Griffin-Lim and FGLA in phase retrieval tasks.

The convergence guarantee is rigorously established.

Abstract

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.