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Summary form only given. Bayesian hierarchical models provide a natural and effective means of exploiting prior knowledge concerning the time-frequency structure of natural sound signals - something that has often been overlooked in traditional approaches to audio signal processing. Having constructed a Bayesian model and prior distributions capable of taking into account the time-frequency characteristics of typical audio waveforms, we focus here on the development of particle filtering algorithms for sequential block-based processing with low latency. We present results for the enhancement of degraded speech and music signals, and compare these with those of a Gabor regression scheme using Markov chain Monte Carlo methods.