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Erschienen in:
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2017 | OriginalPaper | Buchkapitel

On the Use of Latent Mixing Filters in Audio Source Separation

verfasst von : Laurent Girin, Roland Badeau

Erschienen in: Latent Variable Analysis and Signal Separation

Verlag: Springer International Publishing

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Abstract

In this paper, we consider the underdetermined convolutive audio source separation (UCASS) problem. In the STFT domain, we consider both source signals and mixing filters as latent random variables, and we propose to estimate each source image, i.e. each individual source-filter product, by its posterior mean. Although, this is a quite straightforward application of the Bayesian estimation theory, to our knowledge, there exist no similar study in the UCASS context. In this paper, we discuss the interest of this estimator in this context and compare it with the conventional Wiener filter in a semi-oracle configuration.

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Vorheriges Kapitel Psychophysical Evaluation of Audio Source Separation Methods
Nächstes Kapitel Discriminative Enhancement for Single Channel Audio Source Separation Using Deep Neural Networks
Fußnoten
1
A source image is defined as the multichannel version of the source signal, as recorded at the microphones [5].
 
2
Considering the filters as latent variables enables us to make them depend on the time frame \(\ell \) at no additional cost, compared to frame-independent latent filters \(\mathbf {A}_{f}\), given that both models have the same set of parameters. This also comes at a much lower cost than the parametric case. However this does not necessarily mean that we have “trajectories” of filters, as for the moving sources or moving sensors in [7, 9]. This simply allows the realization of the filters to be different for each frame, e.g. modeling slight movements of sources around their mean position. In the following, \(\mathbf {a}_{j,f\ell }\) is assumed wide-sense stationary (WSS) along \(\ell \), hence its mean and covariance matrix do not depend on \(\ell \).
 
3
The proper complex Gaussian distribution is defined as \(\mathcal {N}_c(\mathbf {x};{\varvec{\mu }},{\varvec{\varSigma }}) = {|\pi {\varvec{\varSigma }}|^{-1}} \exp \big ( - [\mathbf {x}-{\varvec{\mu }}]^{\text {H}}{\varvec{\varSigma }}^{-1} [\mathbf {x}-{\varvec{\mu }}] \big )\), where |.| denotes the matrix determinant [14].
 
6
So far, no statistical test could be performed on a large set of mixtures to test the significativity of the results because of the huge computational cost of the Metropolis.
 
Literatur
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Vincent, E., Jafari, M., Abdallah, S., Plumbley, M., Davies, M.: Probabilistic modeling paradigms for audio source separation. In: Machine Audition: Principles, Algorithms and Systems, pp. 162–185 (2010)
2.
Ozerov, A., Févotte, C.: Multichannel nonnegative matrix factorization in convolutive mixtures for audio source separation. IEEE Trans. Audio Speech Lang. Process. 18(3), 550–563 (2010)CrossRef
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Duong, N., Vincent, E., Gribonval, R.: Under-determined reverberant audio source separation using a full-rank spatial covariance model. IEEE Trans. Audio Speech Lang. Process. 18(7), 1830–1840 (2010)CrossRef
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Ozerov, A., Vincent, E., Bimbot, F.: A general flexible framework for the handling of prior information in audio source separation. IEEE Trans. Audio Speech Lang. Process. 20(4), 1118–1133 (2012)CrossRef
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Sturmel, N., Liutkus, A., Pinel, J., Girin, L., Marchand, S., Richard, G., Badeau, R., Daudet, L.: Linear mixing models for active listening of music productions in realistic studio conditions. In: Convention of the Audio Engineering Society (AES). Budapest, Hungary (2012)
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Duong, N., Vincent, E., Gribonval, R.: Spatial location priors for Gaussian model based reverberant audio source separation. EURASIP J. Adv. Signal Process. 149, 2013 (2013)
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Higuchi, T., Takamune, N., Tomohiko, N., Kameoka, H.: Underdetermined blind separation and tracking of moving sources based on DOA-HMM. In: Proceedings of the International Conference on Acoustics, Speech and Signal Proceedings (ICASSP) (2014)
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Leglaive, S., Badeau, R., Richard, G.: Multichannel audio source separation with probabilistic reverberant modeling. In IEEE Workshop Applications of Signal Processing to Audio and Acoustics (WASPAA) (2015)
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Kounades-Bastian, D., Girin, L., Alameda-Pineda, X., Gannot, S., Horaud, R.: A variational EM algorithm for the separation of moving sound sources. In: IEEE Workshop Application Signal Process. to Audio and Acoustics (WASPAA) (2015)
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Smidl, V., Quinn, A.: The Variational Bayes Method in Signal Processing. Springer, Berlin (2006)
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Cemgil, A., Févotte, C., Godsill, S.: Variational and stochastic inference for Bayesian source separation. Digit. Signal Proc. 2007(17), 891–913 (2007)CrossRef
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Liang, F., Liu, C., Carroll, R.: Advanced Markov Chain Monte Carlo Methods: Learning from Past Samples. Wiley, New York (2010)CrossRefMATH
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Gannot, S., Moonen, M.: On the application of the unscented Kalman filter to speech processing. In: IEEE International Workshop on Acoustic Echo and Noise Control (IWAENC), Japan, Kyoto, p. 811(2003)
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Neeser, F., Massey, J.: Proper complex random processes with applications to information theory. IEEE Trans. Info. Theory 39(4), 1293–1302 (1993)MathSciNetCrossRefMATH
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Garofolo, J.S., Lamel, L.F., Fisher, W.M., Fiscus, J.G., Pallett, D.S., Dahlgren, N.L., Zue, V.: TIMIT acoustic-phonetic continuous speech corpus. In: Linguistic Data Consortium, Philadelphia (1993)
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Vincent, E., Sawada, H., Bofill, P., Makino, S., Rosca, J.P.: First stereo audio source separation evaluation campaign: data, algorithms and results. In: Davies, M.E., James, C.J., Abdallah, S.A., Plumbley, M.D. (eds.) ICA 2007. LNCS, vol. 4666, pp. 552–559. Springer, Heidelberg (2007). doi:10.​1007/​978-3-540-74494-8_​69 CrossRef
Metadaten
Titel
On the Use of Latent Mixing Filters in Audio Source Separation
verfasst von
Laurent Girin
Roland Badeau
Copyright-Jahr
2017
Buch
Latent Variable Analysis and Signal Separation

Print ISBN: 978-3-319-53546-3

Electronic ISBN: 978-3-319-53547-0

Copyright-Jahr: 2017

DOI
https://doi.org/10.1007/978-3-319-53547-0_22