Phase reconstruction from amplitude spectrograms
based on von-Mises-distribution deep neural network
Shinnosuke Takamichi*1, Yuki Saito*1, Norihiro Takamune*1, Daichi Kitamura*2, and Hiroshi Saruwatari*1*1: Univ. of Tokyo, Japan, *2: National Institute of Tech., Kagawa College, Japan

Hypothesis: phase reconstruction from amplitude spectrograms based on DNNs
 Phase reconstruction
Griffin-Lim phase reconstruction method[1]provides unnatural artifacts in speech.
Griffin-Lim method [1] Audio signal processing often processes amplitude spectrograms.
 Speech synthesis is shifting from vocoder params. to amplitudes.

 DNN-based phase reconstruction
 Can we train DNNs to predict the phase?
 Isotropic-Gaussian-distribution DNN (mean squared error training) is
not suitable because phase is a periodic variable.

A phase reconstruction method by iterating STFT andinverse STFT.

 Our approach Propose a novel DNN that has the von Mises distribution which is a probability distribution for a periodic variable.
 Introduce group delays that has strong relationship to the amplitude of speech.
1) DNN can predict group delay accurately more than phases, and2) our methods achieve better speech quality than the conventional Griffin-Lim method.

Proposed method: von-Mises-distribution DNN-based phase reconstruction
von Mises distribution and DNN-based phase reconstruction𝒙𝑡

 von Mises (vM) distribution[3]  DNN-based phase reconstruction
𝑃 y; 𝜇, 𝜅 = 𝑒 𝜅 cos 𝑦−𝜇 /2𝜋𝐼0 𝜅𝜇: mean, 𝜅: cnocentration
𝐼0 ⋅ : Modified Bessel function

𝒚𝑡𝒚𝑡 DNN that convert an amplitude 𝒙𝑡 tophase 𝒚𝑡 (𝑡 is the frame index.)
 Loss for DNN training Negative log likelihood (𝜇: parameter)  Phase loss derived from vM dist.
 −log 𝑃 y; 𝜇, 𝜅 ∝ − cos 𝑦 − 𝜇 Group-delay lossΔ𝒚𝒕Δ𝒚𝑡1) Phase loss2) Group-delay loss

 Maximum likelihood estimation of vM distribution.

 Approximate group delay with 1st-order difference.

𝐿PH 𝒚𝒕 , 𝒚𝑡 = −𝑓cos 𝑦𝑡,𝑓 − 𝑦𝑡,𝑓𝐿GD 𝒚𝒕 , 𝒚𝑡 = −𝑦𝑡,𝑓 : phase at 𝑡-th frame and 𝑓-th freq. bin𝑓cos Δ𝑦𝑡,𝑓 − Δ𝑦𝑡,𝑓*Group delay andphase of AR models
have strong relationship [3].

Δ𝑦𝑡,𝑓 = − 𝑦𝑡,𝑓+1 − 𝑦𝑡,𝑓 : group delay at 𝑡-th frame and 𝑓-th freq. bin

Evaluation: prediction accuracy, effects to speech quality, and improvements by group delay
Contents
Training / test data
Sampling freq.
Frame shift, FFT taps
DNN input
DNN output
DNN architecture
Post-process

Value/Settings
JSUT speech corpus[4] 5000 / 300 utts.
16 kHz
80 samples (5 ms)，512 samples
Log amplitudes at current±2 frames
Phase (3 types: 0-2kHz, 0-4kHz, 0-8kHz)
Feed-Forward w/ gated activation units
Phase refinement by the Griffin-Lim method1) Prediction accuracy
 Compared systems- PH: Phase loss only
- GD: Group-delay loss only
- PH+GD: Multi-task learning

 Evaluation method- Cosine distance Results- Group delay is estimatedaccurately more than phase.

2) Speech quality
 Evaluation methods- Preference AB tests onspeech quality

Preference AB tests by 30 listeners
on crowdsourcing

 Results- Better than Griffin-Lim- Multi-task learning achieves better in all
settings3) Improvements by group-delay loss Speech quality- Better than phase loss Convergence in postprocess- Spectral convergence[5] :reconstruction performancethrough STFT & inverse STFT
- Group-delay loss provides
phases that are closest to theperfect reconstruction

Reference[1] Griffin et al., IEEE Trans., 1984.
[2] Bishop, Springer, 2006.
[5] Sturmel et al., Intl. Conf. on Digital Audio Effects, 2011.

Saruwatari Lab., The University of Tokyo[3] Itakura et al., Proc. ICASSP, 1987.

IWAENC2018, Tokyo, Japan[4] Sonobe et al., arXiv, 2007.

2018@Shinnosuke Takamichi Sep. 18, 2018