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Audio Signal Modelling Using Bayesian Atomic Decompositions

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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