Comparing solution methodologies for speech enhancement within a Bayesian framework
Speech enhancement is the area of speech processing concerned with the reconstruction of speech corrupted by some noise process. This report states the problem of enhancing speech corrupted by additive white Gaussian noise within a model-based Bayesian framework, and proceeds to develop and compare three strategies to estimate the model parameters and the clean speech. Each of these methods estimates the additive noise variance from the observed noise corrupted data, alongside the speech model parameters, eliminating the need for off-line estimation of this value. The first two methods are the Evidence Maximisation and Expectation Maximisation (EM) algorithms, which essentially perform maximum a posteriori (MAP) estimation of the model parameters, and, based on this estimate, reconstruct the clean speech. The difference between these two methods lies in the fact that the former performs the maximisation directly in the parameter space, whereas the latter iteratively max-imises for the parameters by conditioning on the current estimate of the clean speech. The third method entertained is the Gibbs sampler, which is a special case of the general class of Markov chain Monte Carlo (MCMC) algorithms. In contrast with the first two methods, which are deterministic, the Gibbs sampler is essentially stochastic in nature, and sets up a Markov chain that generates samples from the joint posterior distribution for the model parameters and clean speech. These samples are subsequently used to calculate Monte Carlo estimates for the desired quantities. The methods are evaluated and compared on real speech corrupted by both stationary and non-stationary noise processes.