Integrating Kalman filtering and multi-pulse coding for speech enhancement with a non-stationary model of the speech signal

In this paper, speech enhancement via Kalman filtering is considered. A non-stationary signal model for the speech signal is first described. This model consists of a slowly varying AR model and an excitation source that exhibits a rapidly time-varying variance. The AR model and the excitation model fit nicely into the Kalman filtering framework, fully exploiting the capability of the Kalman filter to process non-stationary signals in an LMMSE optimum manner. The AR-model coefficients are estimated by a decision-directed type power spectral subtraction method followed by an LPC analysis. For the robust estimation of the rapidly time-varying excitation model in the presence of noise, we propose the use of a multi-pulse linear predictive coding (MPLPC) based method. The Kalman filtering algorithm based on the non-stationary signal model is able to partially avoid the commonly used quasi-stationarity assumption of the speech. Therefore the non-stationarity of the signal is fully exploited in suppressing the noise power that is more stationary. Our experiments show that the Kalman filter with rapidly time-varying variance modeling using the proposed MPLPC based method brings significant performance improvement both when compared to a baseline Kalman filtering method with quasi-stationarity assumption and when compared to the well-known MMSE log-spectral amplitude estimator (MMSE-LSA).