Perceptually enhanced blind single-channel music source separation by Non-negative Matrix Factorization

We propose a new approach that improves perceptual quality of the separated sources in blind single-channel musical source separation. It uses the advantages of subspace learning based on Non-negative Matrix Factorization (NMF) in which the bases represent the notes. The cost function is formulated in the form of weighted β-divergence by adopting the PEAQ auditory model defined in ITU-R BS.1387 into the source separation. The proposed perceptually weighted factorization scheme is integrated into the Non-negative Matrix Factor 2-D Deconvolution (NMF2D) and Clustered Non-negative Matrix Factorization (CNMF) to overcome the source clustering problem encountered in under-determined source separation. It is shown that the introduced perceptually weighted NMF schemes, named as PW-NMF2D and PW-CNMF, efficiently learn the bases that enable us to apply a simple resynthesis of the musical sources based on the temporal model stored in the encoding matrix. Source separation performance has been reported on musical mixtures where 1-2 dB improvement is achieved in terms of SDR, SIR and SAR compared to the state-of-the-art methods. Performance has also been evaluated by perceptual measures resulting an improvement of 2-5 in OPS, TPS, IPS and APS values.