β-divergence two-dimensional sparse nonnegative matrix factorization for audio source separation

In this paper, a novel sparse two dimensional nonnegative matrix factorization (SNMF2D) with the β-divergence is proposed. In SNMF2D, the time-frequency (TF) profile of each source is modeled as two-dimensional convolution of the temporal code and the spectral basis. Sparsity constraint was imposed to reduce the ambiguity and provide uniqueness to the solution. The proposed model maximises the joint probability of the mixing spectral basis and temporal codes conditioned on the mixed signal using multiplicative update rules. Experimental tests have been conducted in audio application to blindly separate the source in musical mixture. Results have concretely shown the efficacy of the algorithm in separating the audio sources from single channel mixture.