# An Investigation on Combining Geometry and Consistency Constraints into Phase Estimation for Speech Enhancement

arXiv: https://arxiv.org/abs/2507.02192 · HTML: https://mlsanity.com/paper/2507.02192/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jul 2025.

## Built on by (most cited first, 1 of 1)

- [CIS-BWE: Chaos-Informed Speech Bandwidth Extension](https://mlsanity.com/paper/2507.15970/) (2025)

## Abstract (arXiv)

We propose a novel iterative phase estimation framework, termed multi-source Griffin-Lim algorithm (MSGLA), for speech enhancement (SE) under additive noise conditions. The core idea is to leverage the ad-hoc consistency constraint of complex-valued short-time Fourier transform (STFT) spectrograms to address the sign ambiguity challenge commonly encountered in geometry-based phase estimation. Furthermore, we introduce a variant of the geometric constraint framework based on the law of sines and cosines, formulating a new phase reconstruction algorithm using noise phase estimates. We first validate the proposed technique through a series of oracle experiments, demonstrating its effectiveness under ideal conditions. We then evaluate its performance on the VB-DMD and WSJ0-CHiME3 data sets, and show that the proposed MSGLA variants match well or slightly outperform existing algorithms, including direct phase estimation and DNN-based sign prediction, especially in terms of background noise suppression.