MMSE-Optimal Spectral Amplitude Estimation Given the STFT-Phase

In this letter, we derive a minimum mean squared error (MMSE) optimal estimator for clean speech spectral amplitudes, which we apply in single channel speech enhancement. As opposed to state-of-the-art estimators, the optimal estimator is derived for a given clean speech spectral phase. We show that the phase contains additional information that can be exploited to distinguish outliers in the noise from the target signal. With the proposed technique, incorporating the phase can potentially improve the PESQ-MOS by 0.5 in babble noise as compared to state-of-the-art amplitude estimators. In a blind setup we achieve a PESQ improvement of around 0.25 in voiced speech.