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

arXiv: https://arxiv.org/abs/2306.12504 · HTML: https://mlsanity.com/paper/2306.12504/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2023.

## Built on by (most cited first, 2 of 2)

- [Generative Adversarial Network based Voice Conversion: Techniques, Challenges, and Recent Advancements](https://mlsanity.com/paper/2504.19197/) (2025)
- [DDFAD: Dataset Distillation Framework for Audio Data](https://mlsanity.com/paper/2407.10446/) (2024)

## Abstract (arXiv)

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.