Speech spectral modeling and enhancement based on autoregressive conditional heteroscedasticity models

Abstract

In this paper, we develop and evaluate speech enhancement algorithms, which are based on supergaussian generalized autoregressive conditional heteroscedasticity (GARCH) models in the short-time Fourier transform (STFT) domain. We consider three different statistical models, two fidelity criteria, and two approaches for the estimation of the variances of the STFT coefficients. The statistical model is either Gaussian, Gamma or Laplacian; the fidelity criteria include minimum mean-squared error (MMSE) of the STFT coefficients and MMSE of the log-spectral amplitude (LSA); the spectral variance is estimated based on either the proposed GARCH models or the decision-directed method of Ephraim and Malah. We show that estimating the variance by the GARCH modeling method yields lower log-spectral distortion and higher perceptual evaluation of speech quality scores (PESQ, ITU-T P.862) than by using the decisiondirected method, whether the presumed statistical model is Gaussian, Gamma or Laplacian, and whether the fidelity criterion is MMSE of the STFT coefficients or MMSE of the LSA. furthermore while a gaussian model is inferior to the supergaussian models when USING the decision-directed method, the Gaussian model is superior when using the garch modeling method. r 2005 Published by Elsevier B.V.

Minimum Mean-Square Error Estimation of Discrete Fourier Coefficients With Generalized Gamma Priors

“…The independency assumption in the complex domain is also inconsistent with the data. We think further improvements in speech enhancement performance are still possible by considering more sophisticated pdf models and better spectral variance estimators [15], [31], [32] simultaneously. For certain types of distortions, other methods may be more appropriate.…”

“…We see that for small arguments, is approximated well by only a few terms. Substituting (15) into (14) (15) converges and because changing the order of integration and summation as is used in the derivation of (16) is allowed for according to Fubini's theorem [22].…”

“…Further, the Wiener estimator (x) provides the weakest SNR-S versus SNR-N tradeoff; as discussed in Section II, this suggests that the speech distribution conditional on the estimated a priori SNR is not well described by a Gaussian model. The Gaussian model and thus the Wiener estimator may perform better for a different a priori SNR estimator [15]. Also, rather simple modifications of the Wiener estimator have been proposed which significantly boost its performance (see, e.g., [29] and [30,Ch.…”

“…Hence, it is important to notice that the appropriate distributional assumption is related to the speech variance estimator used. For example, Cohen [15] suggests that for a different a priori SNR estimator based on GARCH models, the Gaussian speech model is superior. A slight preference for complex Gaussian distributions has also been found for the DFT-coefficients from short analysis frames of individual speech sound classes (vowels, plosives, fricatives, etc.)…”

A CASA-Based System for Long-Term SNR Estimation

“…The a priori SNR, which is the ratio of the speech and noise power, is widely used in speech enhancement algorithms and is typically estimated using the decision-directed approach of Ephraim and Malah [6]. Alternative techniques are based on GARCH models [4] and cepstro-temporal smoothing [3].…”