Bayesian group sparse learning for music source separation

Nonnegative matrix factorization (NMF) is developed for parts-based representation of nonnegative signals with the sparseness constraint. The signals are adequately represented by a set of basis vectors and the corresponding weight parameters. NMF has been successfully applied for blind source separation and many other signal processing systems. Typically, controlling the degree of sparseness and characterizing the uncertainty of model parameters are two critical issues for model regularization using NMF. This paper presents the Bayesian group sparse learning for NMF and applies it for single-channel music source separation. This method reconstructs the rhythmic or repetitive signal from a common subspace spanned by the shared bases for the whole signal and simultaneously decodes the harmonic or residual signal from an individual subspace consisting of separate bases for different signal segments. A Laplacian scale mixture distribution is introduced for sparse coding given a sparseness control parameter. The relevance of basis vectors for reconstructing two groups of music signals is automatically determined. A Markov chain Monte Carlo procedure is presented to infer two sets of model parameters and hyperparameters through a sampling procedure based on the conditional posterior distributions. Experiments on separating single-channel audio signals into rhythmic and harmonic source signals show that the proposed method outperforms baseline NMF, Bayesian NMF, and other group-based NMF in terms of signal-to-interference ratio.