Sparse linear regression with structured priors and application to denoising of musical audio.
Févotte, C et Torrésani, B et Daudet, L et Godsill, S.j. (2008) Sparse linear regression with structured priors and application to denoising of musical audio. In: Journée représentations parcimonieuses du GDR ISIS, 17 Apr 2008, Paris, France.
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Résumé
In this presentation, we describe an audio denoising technique based on sparse linear regression with structured priors. The noisy signal is decomposed as a linear combination of atoms belonging to two Modified Discrete Cosine Transform (MDCT) bases, plus a residual part containing the noise. One MDCT basis has a long time resolution, and thus high frequency resolution, and is aimed at modeling tonal parts of the signal, while the other MDCT basis has short time resolution and is aimed at modeling transient parts (such as attacks of notes). The problem is formulated within a Bayesian setting. Conditionally upon an indicator variable which is either 0 or 1, one expansion coefficient is set to zero or given a hierarchical prior. Structured priors are employed for the indicator variables; using two types of Markov chains, persistency along the time axis is favored for expansion coefficients of the tonal layer, while persistency along the frequency axis is favored for the expansion coefficients of the transient layer. Inference about the denoised signal and model parameters is performed using a Gibbs sampler, a standard Markov chain Monte Carlo (MCMC) sampling technique. We present results for denoising of a short glockenspiel excerpt and a long polyphonic music excerpt. Our approach is compared with unstructured sparse regression and with structured sparse regression in a single resolution MDCT basis (no transient layer). The results show that better denoising is obtained, both from SNR measurements and from subjective criteria, when both a transient and tonal layer are used, in conjunction with our proposed structured prior framework.
| Type d'EPrint: | Document issu d'une conférence ou d'un atelier (Conférence) |
|---|---|
| Date: | 17 Avril 2008 |
| Fonds: | GdR ISIS |
| Titre de la manifestation: | Journée représentations parcimonieuses du GDR ISIS |
| Dates de la manifestation: | 17 Apr 2008 |
| Sujets: | 2. Sciences et technologies de l'information et de la communication 1. Mathématiques et leurs applications |
| Code ID: | 3679 |
| Déposé par : | Remi Gribonval |
| Déposé le : | 22 Mai 2008 |
Références Bibliographiques
C. Févotte, B. Torrésani, L. Daudet, and S. J. Godsill. "Sparse linear regression with structured priors and application to denoising of musical audio," IEEE Trans. Audio, Speech and Language Processing, to appear.
http://www.tsi.enst.fr/~fevotte/Journals/ieee_asl_sparsereg_struc.pdf
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