Bayesian short-time spectral amplitude estimators for single-channel speech enhancement

Single-channel speech enhancement algorithms are used to remove background noise in speech. They are present in many common devices such as cell phones and hearing aids. In the Bayesian short-time spectral amplitude (STSA) approach for speech enhancement, an estimate of the clean speech STSA is derived by minimizing the statistical expectation of a chosen cost function. Examples of such estimators are the minimum mean square error (MMSE) STSA, the β-order MMSE STSA (β-SA), which includes a power law parameter, and the weighted Euclidian (WE), which includes a weighting parameter. This thesis analyzes single-channel Bayesian STSA estimators for speech enhancement with the aim of, firstly, gaining a better understanding of their properties and, secondly, proposing new cost functions and statistical models to improve their performance. In addition to a novel analysis of the β-SA estimator for parameter β ≤ 0, three new families of estimators are developed in this thesis: the Weighted β-SA (Wβ-SA), the Generalized Weighted family of STSA estimators (GWSA) and a family of multi-dimensional Bayesian STSA estimators. The Wβ-SA combines the power law of the β-SA and the weighting factor of the WE. Its parameters are chosen based on the characteristics of the human auditory system which is found to have the advantage of improving the noise reduction at high frequencies while limiting the speech distortions at low frequencies. An analytical generalization of a cost function structure found in many existing Bayesian STSA estimators is proposed through the GWSA family of estimators. This allows a unification of Bayesian STSA estimators and, moreover, provides a better understanding of this general class of estimators. Finally, we propose a multi-dimensional family of estimators that accounts for the correlated frequency components in a digitized speech signal. In fact, the spectral components of the clean speech are traditionally assumed uncorrelated in Bayesian STSA estimators, however, this assumption is inexact since some correlation is present in practice. Objective and subjective experiments are performed in different noise environments and at several signal-to-noise ratios (SNR). Results show the superiority of the proposed estimators over benchmark estimators.