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Audio Signal Modelling Using Bayesian Atomic Decompositions

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We present an investigation into signal processing models appropriate for audio, and especially high quality musical signals, by means of Bayesian atomic decompositions. At present, many models rely on short-term stationarity of the audio, or highly limiting forms of non-stationarity. Moreover, they are well-suited only to low-level inference tasks. We seek to formulate a new generation of audio models that will address the main limitations of the existing ones and permit high-level inference. As we show, such models result from the marriage of an overcomplete dictionary of time-frequency atoms with structured hierarchical prior probability distributions developed specifically for audio signals, in order to model coefficient correlation in time and frequency.

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