Enforcing sparsity, shift-invariance and positivity in a bayesian model of polyphonic piano music

In this paper we develop a Bayesian method to extract individual notes from a polyphonic piano recording. The distribution of the note activation is non-negative and we therefore introduce a modified Rayleigh distribution to model this note behaviour. Sparseness of the note activation is achieved by a mixture distribution that is a mixture of a delta function and the modified Rayleigh distribution. The used learning rule requires integration over the note activations, which is done using a Gibbs sampling Monte Carlo method. We analyse the behaviour of the algorithm using a simplified test signal as well as a real piano recording