MMSE-optimal enhancement of complex speech coefficients with uncertain prior knowledge of the clean speech phase

In most STFT-based speech enhancement algorithms only the STFT amplitude of speech is processed, while the STFT phase of the noisy signal is neither modified nor employed to improve amplitude estimation. This is also, because modifying the spectral phase often yields undesired artifacts and unnatural sounding speech. In this paper, we first obtain a clean speech phase estimate using a recent phase reconstruction algorithm. Then, we propose to treat this reconstructed phase as uncertain a priori knowledge when deriving a joint MMSE estimate of the clean speech amplitude and phase. The resulting MMSE-estimator yields a compromise between the phase of the noisy signal and the prior phase estimate. Instrumental measures and informal listening show that the proposed estimator reduces un-desired artifacts and results in an improved speech quality.