A tractable framework for estimating and combining spectral source models for audio source separation

Abstract

International audienceThe underdetermined blind audio source separation (BSS) problem is often addressed in the time-frequency (TF) domain assuming that each TF point is modeled as an independent random variable with sparse distribution. On the other hand, methods based on structured spectral model, such as the Spectral Gaussian Scaled Mixture Models (Spectral-GSMMs) or Spectral Non-negative Matrix Factorization models, perform better because they exploit the statistical diversity of audio source spectrograms, thus allowing to go beyond the simple sparsity assumption. However, in the case of discrete state-based models, such as Spectral-GSMMs, learning the models from the mixture can be computationally very expensive. One of the main problems is that using a classical Expectation-Maximization procedure often leads to an exponential complexity with respect to the number of sources. In this paper, we propose a framework with a linear complexity to learn spectral source models (including discrete state-based models) from noisy source estimates. Moreover, this framework allows combining di erent probabilistic models that can be seen as a sort of probabilistic fusion. We illustrate that methods based on this framework can significantly improve the BSS performance compared to the state-of-the-art approaches

The signal separation evaluation campaign (2007–2010): Achievements and remaining challenges

“…The results support the emergence of source separation systems exploiting advanced source models accounting for the source spectra in the case of audio source separation [22,23,24,30] or for signaling pathway information in the case of biomedical source separation [34]. Nevertheless, more conventional methods based on frequency-domain ICA or SCA still perform best on live audio recordings of many sources and/or background noise [25,27,28,29].…”

“…• Performance drops on 4-channel mixtures of 4 sources, for which the best 4-channel 2-source separation method [27] achieves a SIR of 3 dB only, and on professionally produced music recordings, for which the best method [30] based on the aforementioned variance modeling framework provided a SIR of 9 dB. This suggests that performance does not depend so much whether the mixture is determined or overdetermined but rather on the number of sources itself, since a larger number of sources makes it more difficult to achieve accurate source localization, which is a prerequisite in most source separation methods.…”

Automatic music transcription: challenges and future directions

“…In this case, the separation task is underdetermined, and can only be solved by making some assumptions about the sources. These may include sparsity, non-negativity and independence, or may take the form of structured spectral models like NMF models [60], PLCA models [6], spectral Gaussian scaled mixture models (Spectral-GSMMs) [2] or the source-filter model for sound production [62]. Further constraints such as temporal continuity or harmonicity can be employed together with spectral models.…”

An interactive audio source separation framework based on non-negative matrix factorization

“…Also, the latter is crucial so as to account for the well-separated regions where artifacts and interferences still remain from the previous separation step 2 . To fulfil this challenge, we exploit uncertainty-based learning [12,13] where source models can be learned from the source estimates, while taking into account separation errors described by their variances. The principle is summarized as follow.…”

“…The principle is summarized as follow. Within the above-mentioned Gaussian assumption, the posterior of j-th source writes [12] p(s j,f n |x f n ; θ) = Nc s j,f n ;ŝ j,f n ,v…”