Multichannel HR-NMF for modelling convolutive mixtures of non-stationary signals in the time-frequency domain

Several probabilistic models involving latent components have been proposed for modelling time-frequency (TF) representations of audio signals (such as spectrograms), notably in the nonnegative matrix factorization (NMF) literature. Among them, the recent high resolution NMF (HR-NMF) model is able to take both phases and local correlations in each frequency band into account, and its potential has been illustrated in applications such as source separation and audio inpainting. In this paper, HR-NMF is extended to multichannel signals and to convolutive mixtures. A fast variational expectation-maximization (EM) algorithm is proposed to estimate the enhanced model. This algorithm is applied to a stereophonic piano signal, and proves capable of accurately modelling reverberation and restoring missing observations.