Statistical reconstruction and analysis of autoregressive signals in impulsive noise using the Gibbs sampler

Modeling and reconstruction methods are presented for noise reduction of autocorrelated signals in non-Gaussian, impulsive noise environments. A Bayesian probabilistic framework is adopted and Markov chain Monte Carlo methods are developed for detection and correction of impulses. Individual noise sources are modeled as Gaussian with unknown scale (variance), allowing for robustness to "heavy-tailed" impulse distributions, while the underlying signal is modeled as autoregressive (AR). Results are presented for both artificial and real data from voice and music recordings, and comparisons are made with existing techniques. The new techniques are found to give improved detection and elimination of impulses in adverse noise conditions at the expense of some extra computational complexity.