# Phase reconstruction from amplitude spectrograms based on von-Mises-distribution deep neural network

arXiv: https://arxiv.org/abs/1807.03474 · HTML: https://mlsanity.com/paper/1807.03474/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jul 2018.

## Built on by (most cited first, 6 of 6)

- [Vocos: Closing the gap between time-domain and Fourier-based neural vocoders for high-quality audio synthesis](https://mlsanity.com/paper/2306.00814/) (2023)
- [DiffPhase: Generative Diffusion-based STFT Phase Retrieval](https://mlsanity.com/paper/2211.04332/) (2022)
- [A Survey of Deep Learning for Complex Speech Spectrograms](https://mlsanity.com/paper/2505.08694/) (2025)
- [EDNet: A Versatile Speech Enhancement Framework with Gating Mamba Mechanism and Phase Shift-Invariant Training](https://mlsanity.com/paper/2506.16231/) (2025)
- [Stage-Wise and Prior-Aware Neural Speech Phase Prediction](https://mlsanity.com/paper/2410.04990/) (2024)
- [Efficient Neural and Numerical Methods for High-Quality Online Speech Spectrogram Inversion via Gradient Theorem](https://mlsanity.com/paper/2505.24498/) (2025)

## Abstract (arXiv)

This paper presents a deep neural network (DNN)-based phase reconstruction from amplitude spectrograms. In audio signal and speech processing, the amplitude spectrogram is often used for processing, and the corresponding phase spectrogram is reconstructed from the amplitude spectrogram on the basis of the Griffin-Lim method. However, the Griffin-Lim method causes unnatural artifacts in synthetic speech. Addressing this problem, we introduce the von-Mises-distribution DNN for phase reconstruction. The DNN is a generative model having the von Mises distribution that can model distributions of a periodic variable such as a phase, and the model parameters of the DNN are estimated on the basis of the maximum likelihood criterion. Furthermore, we propose a group-delay loss for DNN training to make the predicted group delay close to a natural group delay. The experimental results demonstrate that 1) the trained DNN can predict group delay accurately more than phases themselves, and 2) our phase reconstruction methods achieve better speech quality than the conventional Griffin-Lim method.