A BAYESIAN-ESTIMATION APPROACH FOR SPEECH ENHANCEMENT USING HIDDEN MARKOV-MODELS

A Bayesian estimation approach for enhancing speech signals which have been degraded by statistically independent additive noise is motivated and developed. In particular, minimum mean square error (MMSE) and maximum a posteriori (MAP) signal estimators are developed using hidden Markov models (HMM's) for the clean signal and the noise process. It is shown that the MMSE estimator comprises a weighted sum of conditional mean estimators for the composite states of the noisy signal (pairs of states of the models for the signal and noise), where the weights equal the posterior probabilities of the composite states given the noisy signal. The estimation of several spectral functions of the clean signal such as the sample spectrum and the complex exponential of the phase is also considered. A gain-adapted MAP estimator is developed using the expectation-maximization (EM) algorithm. In this approach an HMM for gain-normalized clean signals is estimated from the training data, and the signal and its gain contour are estimated from the noisy signal using the MAP estimation approach. The theoretical performance of the MMSE estimator is discussed, and convergence of the MAP estimator is proved. Both the MMSE and MAP estimators are tested in enhancing speech signals degraded by white Gaussian noise at input signal-to-noise ratio of from 5 to 20 dB.