Speech enhancement using a minimum-mean square error short-time spectral amplitude estimator

Abstract

Absstroct-This paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short-time spectral amplitude (STSA) of the speech signal in its perception. A system which utilizes a minimum mean-square error (MMSE) STSA estimator is proposed and then compared with other widely used systems which are based on Wiener filtering and the "spectral subtraction" algorithm. In this paper we derive the MMSE STSA estimator, based on modeling speech and noise spectral components as statistically independent Gaussian random variables. We analyze the performance of the proposed STSA estimator and compare it with a STSA estimator derived from the Wiener estimator. We also examine the MMSE STSA estimator under uncertainty of signal presence in the noisy observations. In constructing the enhanced signal, the MMSE STSA estimator is combined with the complex exponential of the noisy phase. It is shown here that the latter is the MMSE estimator of the complex exponential of the original phase, which does not affect the STSA estimation. The proposed approach results in a significant reduction of the noise, and provides enhanced speech with colorless residual noise. The complexity of the proposed algorithm is approximately that of other systems in the discussed class.

A generalized estimation approach for linear and nonlinear microphone array post-filters

“…estimation approach [4].This is a single channel method used to estimate the transfer function of the post-filter.…”

“…Since in practice this is not the case and furthermore their measurement is a complicated and cumbersome task, the following assumptions, motivated by the central limit theorem [4], are adopted:…”

“…Thus, it seems more suitable to estimate the speech spectral amplitude instead of the complex spectrum. If we write S(k, ℓ) = A(k, ℓ)e jψ(k,ℓ) where A(k, ℓ) is the short-time spectral amplitude and ψ(k, ℓ) is the phase, then the MMSE-STSA estimator for the kth spectral component, is given by the conditional mean [4]:…”

“…This optimal multichannel MSE filter has been shown in [2,3] that can be factorized into a Minimum Variance Distortionless Response (MVDR) beamformer, followed by a single channel Wiener postfilter. However, the MSE distortion of the signal estimate is essentially not the optimum criterion for speech enhancement [4,5]. More appropriate distortion measures for speech enhancement are based either on the MSE of the spectral amplitude or on the MSE of the log-spectral amplitude, leading to the short-time spectral amplitude (STSA) estimator [4] and the log-spectral amplitude (log-STSA) estimator [5], respectively.…”

“…However, the MSE distortion of the signal estimate is essentially not the optimum criterion for speech enhancement [4,5]. More appropriate distortion measures for speech enhancement are based either on the MSE of the spectral amplitude or on the MSE of the log-spectral amplitude, leading to the short-time spectral amplitude (STSA) estimator [4] and the log-spectral amplitude (log-STSA) estimator [5], respectively. These estimators have also been proved to decompose into a MVDR beamformer followed by a single channel post-filter [6].…”