Non-stationary Bayesian modelling and enhancement of speech signals
This report applies time-varying AR (TVAR) models with stochastically evolving parameters to the problem of speech modelling and enhancement. For the TVAR coefficients the standard parameterisation, i.e. the coefficients of the TVAR polynomial themselves, and one i.t.o. the characteristic roots of the TVAR polynomial (or system poles) are investigated. The stochastic evolution models for the TVAR parameters are Markovian diffusion processes. The problem and estimation objectives are formulated within a Bayesian framework. Two efficient iterative algorithms are developed to achieve these objectives. The first is a Markov chain Monte Carlo (MCMC) algorithm which generates samples from the posterior distribution based on which the minimum mean square error (MMSE) estimates of the TVAR parameters and clean speech can be computed. The second is a stochastic optimisation algorithm which computes the marginal maximum a posteriori (MMAP) estimate of the TVAR parameters. The clean speech can then be obtained by running a fixed-interval Kalman smoother with this estimate of the TVAR parameters. Contrary to the EM-type algorithms, the estimation schemes work without introducing a set of " missing data " (the clean speech in this case). Nevertheless, at each iteration the computational complexity of the algorithms is still linear in the number of samples in the analysis window. Performance measures based on predictive distributions are used in simulation studies to compare the modelling and signal reconstruction performance of the proposed TVAR models to that of the standard fixed-parameter AR model on both synthetic and real speech data sets.