Speech enhancement based on perceptually motivated Bayesian estimators of the magnitude spectrum

The traditional minimum mean-square error (MMSE) estimator of the short-time spectral amplitude is based on the minimization of the Bayesian squared-error cost function. The squared-error cost function, however, is not subjectively meaningful in that it does not necessarily produce estimators that emphasize spectral peak (formants) information or estimators which take into account auditory masking effects. To overcome the shortcomings of the MMSE estimator, we propose in this paper Bayesian estimators of the short-time spectral magnitude of speech based on perceptually motivated cost functions. In particular, we use variants of speech distortion measures, such as the Itakura-Saito and weighted likelihood-ratio distortion measures, which have been used successfully in speech recognition. Three classes of Bayesian estimators of the speech magnitude spectrum are derived. The first class of estimators emphasizes spectral peak information, the second class uses a weighted-Euclidean cost function that implicitly takes into account auditory masking effects, and the third class of estimators is designed to penalize spectral attenuation. Of the three classes of Bayesian estimators, the estimators that implicitly take into account auditory masking effect performed the best in terms of having less residual noise and better speech quality.