# Deep Learning Based Phase Reconstruction for Speaker Separation: A Trigonometric Perspective

arXiv: https://arxiv.org/abs/1811.09010 · HTML: https://mlsanity.com/paper/1811.09010/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Nov 2018.

## Built on by (most cited first, 13 of 13)

- [MossFormer: Pushing the Performance Limit of Monaural Speech Separation using Gated Single-Head Transformer with Convolution-Augmented Joint Self-Attentions](https://mlsanity.com/paper/2302.11824/) (2023)
- [CMGAN: Conformer-Based Metric-GAN for Monaural Speech Enhancement](https://mlsanity.com/paper/2209.11112/) (2022)
- [Real-time Denoising and Dereverberation with Tiny Recurrent U-Net](https://mlsanity.com/paper/2102.03207/) (2021)
- [Many-Speakers Single Channel Speech Separation with Optimal Permutation Training](https://mlsanity.com/paper/2104.08955/) (2021)
- [Resource-Efficient Separation Transformer](https://mlsanity.com/paper/2206.09507/) (2022)
- [REAL-M: Towards Speech Separation on Real Mixtures](https://mlsanity.com/paper/2110.10812/) (2021)
- [A Neural State-Space Model Approach to Efficient Speech Separation](https://mlsanity.com/paper/2305.16932/) (2023)
- [Exploring Self-Attention Mechanisms for Speech Separation](https://mlsanity.com/paper/2202.02884/) (2022)
- [UNSSOR: Unsupervised Neural Speech Separation by Leveraging Over-determined Training Mixtures](https://mlsanity.com/paper/2305.20054/) (2023)
- [Deep neural network techniques for monaural speech enhancement: state of the art analysis](https://mlsanity.com/paper/2212.00369/) (2022)
- [A Survey of Deep Learning for Complex Speech Spectrograms](https://mlsanity.com/paper/2505.08694/) (2025)
- [Online Self-Attentive Gated RNNs for Real-Time Speaker Separation](https://mlsanity.com/paper/2106.13493/) (2021)
- [Speech Separation based on Contrastive Learning and Deep Modularization](https://mlsanity.com/paper/2305.10652/) (2023)

## Abstract (arXiv)

This study investigates phase reconstruction for deep learning based monaural talker-independent speaker separation in the short-time Fourier transform (STFT) domain. The key observation is that, for a mixture of two sources, with their magnitudes accurately estimated and under a geometric constraint, the absolute phase difference between each source and the mixture can be uniquely determined; in addition, the source phases at each time-frequency (T-F) unit can be narrowed down to only two candidates. To pick the right candidate, we propose three algorithms based on iterative phase reconstruction, group delay estimation, and phase-difference sign prediction. State-of-the-art results are obtained on the publicly available wsj0-2mix and 3mix corpus.