Abstract

Abstract In this paper, an overview of Bayesian methods and models in signal and image processing is given. The first part of the paper reviews some traditional classes of model employed for signal processing time series analysis. Marginal inference based upon analytic integration of hyperparameters is described for these models and illustrations are given for the problem of estimating sinusoidal frequency components in white Gaussian noise and for the general changepoint problem applied to digital communications. In the second part of the paper, state of the art applications are described which employ MCMC methods for the enhancement of noise-degraded audio signals, non-linear system identification and image sequence restoration. The complex modelling requirements and large datasets involved in these problems require sophisticated MCMC schemes employing efficient blocking schemes, model uncertainty strategies (both reversible jump and Gibbs variable selection) and non-linear/non-Gaussian models.

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