On the decision-directed estimation approach of Ephraim and Malah

The decision-directed approach of Y. Ephraim and D. Malah (IEEE Trans. Acoustics, Speech and Signal Proc., vol.ASSP-32, no.6, p.1109-21, 1984) is widely used for a priori SNR estimation and speech enhancement. However, it conflicts with common model assumptions. We propose recursive estimators for the a priori SNR and the speech spectral components. We introduce a novel statistical model that takes into account the time-correlation between successive speech spectral components, while keeping the resulting algorithms simple. This model provides new insight into the decision-directed approach, and enables the extension of existing speech enhancement algorithms to noncausal estimation. The causal a priori SNR estimator degenerates, as a special case, to a "decision-directed" estimator with a time-varying frequency-dependent weighting factor. The noncausal estimator is capable of discriminating between speech onsets and noise irregularities, achieving lower levels of both musical noise and speech distortion.