Bayesian Enhancement of Speech and Audio Signals which can be Modelled as ARMA Processes

In application areas which involve digitised speech and audio signals, such as coding, digital remastering of old recordings and recognition of speech, it is often desirable to reduce the effects of noise with the aim of enhancing intelligibility and perceived sound quality. We consider the case where noise sources contain non-Gaussian, impulsive elements superimposed upon a continuous Gaussian background. Such a situation arises in areas such as communications channels, telephony and gramophone recordings where impulsive effects might be caused by electromagnetic interference (lightning strikes), electrical switching noise or defects in recording media, while electrical circuit noise or the combined effect of many distant atmospheric events lead to a continuous Gaussian component.
In this paper we discuss the background to this type of noise degradation and describe briefly some existing statistical techniques for noise reduction. We propose new methods for enhancement based upon Markov chain Monte Carlo (MCMC) simulation. Signals are modelled as autoregressive moving-average (ARMA); while noise sources are treated as discrete and continuous mixtures of Gaussian distributions. Results are presented for both real and artificially corrupted data sequences, illustrating the potential of the new methods.