Télécom ParisTech / TSI
37 / 39 rue Dareau
75014 Paris, FRANCE
firstname.lastname (at) telecom-paristech.fr
This talk will present two classes of low-rank matrix approximation methods and their applications to music signals. The first part of the talk will be devoted to subspace-based high resolution (HR) methods, which aim to estimate close frequencies in a mixture of sinusoidal signals. The presentation will focus on new adaptive algorithms, which permit to deal with non-stationary signals in a computationally efficient way, with some applications to music signals (sinusoids/noise separation, beat estimation, audio coding). The second part of the talk will be devoted to nonnegative matrix factorization (NMF), which has proven successful in decomposing musical spectrograms into meaningful elements. The presentation will introduce some improvements to NMF, which permit to better represent harmonic spectra and deal with non-stationarities, with applications to automatic music transcription and source separation.
Nonnegative Matrix Factorization (NMF) is a powerful tool for decomposing mixtures of non-stationary signals in the Time-Frequency (TF) domain. In the literature, a variety of probabilistic models involving latent variables have been designed for introducing some a priori knowledge (like harmonicity and smoothness) into NMF. However, phases are generally ignored in such models, which results in a limited spectral resolution (sinusoids in the same frequency band cannot be properly separated). Moreover, most of these models assume that all TF coefficients are independent, which is not the case of sinusoidal signals for instance. In this talk, I will present a unified probabilistic model called HR-NMF, which achieves a high spectral resolution by taking both phases and local correlations in each frequency band into account. The potential of this new approach will be illustrated in the context of audio source separation and audio inpainting.
High resolution spectral analysis and nonnegative decompositions applied to music signal processing.
Probabilistic modelling of time-frequency representations with application to music signals.