Sparse linear regression with structured priors and application to denoising of musical audio

IEEE Transactions on Audio, Speech and Language Processing

Volumn 16, Issue 1, 2008, Pages 174-185

  Fevotte, Cédric ^a   Torresani, Bruno ^b   Daudet, Laurent ^c   Godsill, Simon J ^d  

^a TELECOM PARISTECH   (France)

^b AIX MARSEILLE UNIVERSITÉ   (France)

^c INSTITUT JEAN LE ROND D ALEMBERT   (France)

^d UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Bayesian variable selection; Denoising; Markov chain Monte Carlo (MCMC) methods; Nonlinear signal approximation; Sparse component analysis; Sparse regression; Sparse representations

Indexed keywords

BAYESIAN VARIABLE SELECTION; DENOISING; MARKOV CHAIN MONTE CARLO (MCMC) METHODS; NONLINEAR SIGNAL APPROXIMATION; SPARSE COMPONENT ANALYSIS; SPARSE REGRESSION; SPARSE REPRESENTATIONS;

AUDIO ACOUSTICS; BAYESIAN NETWORKS; COMPUTERIZED TOMOGRAPHY; COSINE TRANSFORMS; DISCRETE COSINE TRANSFORMS; MARKOV PROCESSES; REGRESSION ANALYSIS; SAMPLING; SECURITY OF DATA; SIGNAL PROCESSING; SIGNAL TO NOISE RATIO; UNCERTAIN SYSTEMS;

MONTE CARLO METHODS;

EID: 51449088121     PISSN: 15587916     EISSN: None     Source Type: Journal    
DOI: 10.1109/TASL.2007.909290     Document Type: Article

References (29)

1. H. S. Malvar, "Lapped transforms for efficient transform/subband coding," IEEE Trans. Acoust., Speech, Signal Process., vol. 38, no. 6, pp. 969-978, Jun. 1990.
2. ISO/IEC 13818-7 (MPEG-2 Advanced Audio Coding, AAC), ISO/IEC 13818-7, Int. Org. Standard., 1997.
3. S. Mallat and S. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
4. S. Chen, D. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SI AM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998.
5. I. F. Gorodnitsky and B. D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A re-weighted minimum norm algorithm," IEEE Trans. Signal Process., vol. 45, no. 3. pp. 600-616, Mar. 1997.
6. B. D. Rao, K. Engan, S. F. Cotter, J. Palmer, and K. Kreutz-Delgado, "Subset selection in noise based on diversity measure minimization," IEEE Trans. Signal Pwcess., vol. 51, no. 3, pp. 760-770, Mar. 2003.
7. M. A. T. Figueiredo, "Adaptive sparseness for supervised learning," IEEE Trans. Pattern Anal. Mach. Intell, vol. 25, no. 9. pp. 1150-1159, Sep. 2003.
8. M. E. Davies and L. Daudet, "Sparse audio representations using the MCLT," Signal Process., vol. 86, no. 3, pp. 457-170, Mar. 2006.
9. C. Févotte and S. J. Godsill, "Sparse linear regression in unions of bases via Bayesian variable selection," IEEE Signal Process. Lett., vol. 13, no. 7. pp. 441-444, Jul. 2006.
10. S. Molla and B. Torrésani, "An hybrid audio scheme using hidden Markov models of waveforms," Appl. Comput. Harmonic Anal, vol. 18, pp. 137-166, 2005.
11. C. Tantibundhit, J. R. Boston, C. Li, J. D. Durrant, S. Shaiman, K. Kovacyk, and A. A. El-Jaroudi, "Speech enhancement using transient speech components," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP06), 2006, pp. I-833-I-836.
12. P. J. Wolfe, S. J. Godsill, and W.-J. Ng, "Bayesian variable selection and regularisation for time-frequency surface estimation," J. R. Statist. Soc. Ser. B, vol. 66, no. 3, pp. 575-589, 2004, read paper (with discussion).
13. P. J. Wolfe and S. J. Godsill, "Interpolation of missing data values for audio signal restoration using a Gabor regression model," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP'05), Mar. 2005, pp. V-517-V-520.
14. L. Daudet and B. Torrésani, "Hybrid representations for audiophonic signal encoding," Signal Process., vol. 82, no. 11, pp. 1595-1617, 2002.
15. C. Févotte and S. Godsill, "A Bayesian approach to blind separation of sparse sources," IEEE Trans. Audio, Speech Lang. Process., vol. 14, no. 6, pp. 2174-2188, Nov. 2006.
16. C. Févotte, L. Daudet, S. J. Godsill, and B. Torrésani, "Sparse regression with structured priors: Application to audio denoising," in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP'06), Toulouse, France, 2006, pp. 111-57-111-60.
17. B. Edler and H. Purnhagen, "Parametric audio coding," in Proc. Int. Conf. Signal Process. (ICSP'00), 2000, pp. 21-24.
18. A. Gelman, J. B. Carlin, H. S. Stern, and D. B. Rubin, Bayesian Data Analysis, ser. Texts in Statistical Science, 2nd ed. London, U.K.: Chapman & Hall/CRC, 2004.
19. S. Geman and D. Geman, "Stochastic relaxation, Gibbs distributions,
20. and the Bayesian restoration of images," IEEE Trans. Pattern Anal. Much. Intel!., vol. PAMI-6, no. 6, pp. 721-741, Nov. 1984.
21. J. Geweke, Variable Selection and Model Comparison in Regression, J. M. Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Swith, Eds., 5th ed. Oxford, U.K.: Oxford Univ. Press, 1996, pp. 609-620.
22. Y. Ephraim and D. Malah, "Speech enhancement using a minimum mean square error short-time spectral amplitude estimator," IEEE Trans. Acoust., Speech, Signal Pwcess., vol. ASSP-32, no. 6, pp. 1109-1121, Dec. 1984.
23. [Online]. Available: http://www.tsi.enst.fr/fevotte/Samples/ieee-asl- denoising/
24. M. Davy and S. Godsill, "Bayesian harmonic models for musical signal analysis," in Seventh Valencia Int. Meeting (Bayesian Statistics VII). Oxford, U.K.: Oxford Univ. Press, 2002.
25. A. Doucet, S. J. Godsill, and C. Andrieu, "On sequential Monte Carlo sampling methods for Bayesian filtering," Statist. Comput., vol. 10, pp. 197-208, 2000.
26. J. Vermaak, C. Andrieu, A. Doucet, and S. J. Godsill, "Particle methods for Bayesian modeling and enhancement of speech signals," IEEE Trans. Speech Audio Process., vol. 10, no. 3, pp. 173-185, Mar. 2002.
27. S. J. Godsill, A. Doucet, and M. West, "Monte Carlo smoothing for non-linear time series," J. Amer. Statist. Assoc., vol. 99, no. 465, pp. 156-168, 2004.
28. S. Molla and B. Torrésani, "An hybrid audio scheme using hidden Markov models of waveforms," Appl. Comput. Harmonic Anal., vol. 18, no. 2, pp. 137-166, Mar. 2005.
29. M. A. Clyde and R. L. Wolpert, "Nonparametric function estimation using overcomplete dictionaries," in Bayesian Statistics VIII, J. Bernardo, J. Berger, A. Dawid, A. Smith, M. West, and D. Heckerman, Eds. Oxford, U.K.: Oxford Univ. Press, 2007, pp. 1-24.