# A Flexible Online Framework for Projection-Based STFT Phase Retrieval

arXiv: https://arxiv.org/abs/2309.07043 · HTML: https://mlsanity.com/paper/2309.07043/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Sep 2023.

## Built on by (most cited first, 3 of 3)

- [Real-Time Streamable Generative Speech Restoration with Flow Matching](https://mlsanity.com/paper/2512.19442/) (2025)
- [Real-Time Streaming Mel Vocoding with Generative Flow Matching](https://mlsanity.com/paper/2509.15085/) (2025)
- [Efficient Neural and Numerical Methods for High-Quality Online Speech Spectrogram Inversion via Gradient Theorem](https://mlsanity.com/paper/2505.24498/) (2025)

## Abstract (arXiv)

Several recent contributions in the field of iterative STFT phase retrieval have demonstrated that the performance of the classical Griffin-Lim method can be considerably improved upon. By using the same projection operators as Griffin-Lim, but combining them in innovative ways, these approaches achieve better results in terms of both reconstruction quality and required number of iterations, while retaining a similar computational complexity per iteration. However, like Griffin-Lim, these algorithms operate in an offline manner and thus require an entire spectrogram as input, which is an unrealistic requirement for many real-world speech communication applications. We propose to extend RTISI -- an existing online (frame-by-frame) variant of the Griffin-Lim algorithm -- into a flexible framework that enables straightforward online implementation of any algorithm based on iterative projections. We further employ this framework to implement online variants of the fast Griffin-Lim algorithm, the accelerated Griffin-Lim algorithm, and two algorithms from the optics domain. Evaluation results on speech signals show that, similarly to the offline case, these algorithms can achieve a considerable performance gain compared to RTISI.