Fully Bayesian Restoration using EM and MCMC
In this chapter we consider the restoration of click-degraded audio using advanced statistical estimation techniques. In the methods of earlier chapters it was generally not possible to eliminate the system hyperparameters such as the AR coefficients and noise variances without losing the analytical tractability of the interpolation and detection schemes; thus heuristic or iterative methods had to be adopted for estimation of these ‘nuisance’ parameters. The methods used here are formalised iterative procedures which allow all of the remaining hyperparameters to be numerically integrated out of the estimation scheme, thus forming estimators for just the quantities of interest, in this case the restored data. These methods, especially the Monte Carlo schemes, are highly computationally intensive and cannot currently be considered for on-line or real time implementation. However, they illustrate that fully Bayesian inference with its inherent advantages can be performed on realistic and sophisticated models given sufficient computational power. In future years, with the advancements in available computational speed which are continually being developed, methods such as these seem likely to dominate statistical signal processing when complex models are required.
KeywordsDust Covariance Autocorrelation Ditioned
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