Bayesian extensions to non-negative matrix factorisation for audio signal modelling

We describe the underlying probabilistic generative signal model of non-negative matrix factorisation (NMF) and propose a realistic conjugate priors on the matrices to be estimated. A conjugate Gamma chain prior enables modelling the spectral smoothness of natural sounds in general, and other prior knowledge about the spectra of the sounds can be used without resorting to too restrictive techniques where some of the parameters are fixed. The resulting algorithm, while retaining the attractive features of standard NMF such as fast convergence and easy implementation, outperforms existing NMF strategies in a single channel audio source separation and detection task.