Bayesian restoration of quantised audio signals using a sinusoidal model with autoregressive residuals

In digital audio systems, the amplitude of the signal is quantised with finite resolution. This is a nonlinear process which introduces distortion. We develop a Bayesian, model-based approach to reducing quantisation distortion when moving an audio signal to a higher resolution medium. The signal is modelled as a sum of sinusoids and an autoregressive (AR) process of unknown order. Estimation is performed using Markov chain Monte Carlo (MCMC) methods. Selection of the correct AR model order and number of sinusoids is found to be crucial to avoiding artefacts; both of these operations are incorporated into the MCMC structure. An approximate, but fast converging, MCMC method is developed for selecting the sinusoids, and moves between AR models of different orders are made using reversible-jump methods.