Random models for sparse signals expansion on unions of bases with application to audio signals

IEEE Transactions on Signal Processing

Volumn 56, Issue 8 I, 2008, Pages 3468-3481

  Kowalski, Matthieu ^a   Torresani, Bruno ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Adaptive thresholding; Denoising; Nonlinear signal approximation; Sparse representations; Time frequency decompositions

Indexed keywords

CLASSIFICATION (OF INFORMATION); COMPUTERIZED TOMOGRAPHY; IMAGE PROCESSING; IMAGING SYSTEMS; IMAGING TECHNIQUES; OPTICAL DATA PROCESSING; PROGRAMMING THEORY; SIGNAL ANALYSIS;

ADAPTIVE THRESHOLDING; AUDIO SIGNALS; BASIS FUNCTIONS; DENOISING; EFFICIENT ESTIMATION; INNER PRODUCTS; LINEAR COMBINATION; NEW APPROACHES; NONLINEAR SIGNAL APPROXIMATION; NUMERICAL EXPERIMENTS; ORTHONORMAL BASES; PROBABILISTIC MODELLING; RANDOM COEFFICIENTS; RANDOM MODELS; SIGNAL EXPANSION; SPARSE REPRESENTATIONS; SPARSE SIGNALS; TIME-FREQUENCY DECOMPOSITIONS; WAVEFORMS;

AUDIO ACOUSTICS;

EID: 48849116494     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2008.920144     Document Type: Article

References (21)

1. S. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. Signal Process., vol. 41, no. 12, pp. 3397-3415, Dec. 1993.
2. G. Teschke, "Multi-frames representations in linear inverse problems with mixed multi-constraints," Appl. Comput. Harmon. Anal., vol. 22, no. 1, pp. 43-60, Jan. 2006.
3. M. A. T. Figueiredo, "Adaptive sparseness for supervised learning," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 9, pp. 1150-1159, Sep. 2003.
4. 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.
5. L. Daudet and B. Torrésani, "Hybrid representations for audiophonic signal encoding," Signal Process. vol. 82, Special Issue on Image and Video Coding Beyond Standards, no. 11, pp. 1595-1617, Nov. 2002.
6. S. Molla and B. Torrésani, "An hybrid audio scheme using hidden Markov models of waveforms," Appl. Comput. Harmon. Anal., vol. 18, no. 2, pp. 137-166, Mar. 2005.
7. M. Vetterli and J. Kovacević, Wavelets and Subband Coding, ser. Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1995.
8. C. Févotte, L. Daudet, S. J. Godsill, and B. Torrésani, "Sparse regression with structured priors: Application to audio denoising," presented at the IEEE Int. Conf. Acoustics, Speech, Audio Signal, Toulouse, France, May 2006.
9. M. Kowalski and B. Torrésani, "A study of Bernoulli and structured random audio models," in Proc. Conf. Signal Process. Adaptive Sparse Structured Representations (SPARS'05), R. Gribonval, Ed., Rennes, France, Nov. 2005, pp. 59-62.
10. M. Kowalski and B. Torrésani, "A family of random waveform models for audio coding," presented at the IEEE Int. Conf. Acoustics, Speech, Audio Signal, Toulouse, France, May 2006.
11. J. A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Trans. Inf. Theory, vol. 50, no. 10, pp. 2231-2242, Oct. 2004.
12. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1964 [Online]. Available: http://www.math.sfu.ca/~cbm/aands/
13. M. A. Stephens, "Tests based on EDF statistics," in Goodness-of-Fit Techniques, R. B. DAgostino and M. A. Stephens, Eds. New York: Marcel Dekker, 1986.
14. G. Govaert and G. Celeux, "A classification EM algorithm for clustering and two stochastic versions," Computat. Statist. Data Anal., vol. 14, no. 3, pp. 315-332, 1992.
15. S. S. Chen, D. L. Donoho, and M. Saunders, "Atomic decomposition by basis pursuit," SIAM J. Sci. Comput., vol. 20, no. 1, pp. 33-61, 1998.
16. B. D. Rao, E. Kjersti, S. F. Cotter, J. Palmer, and K. Kreutz-Delgado, "Subset selection in noise based on diversity measure minimization," IEEE Trans. Signal Process., vol. 51, no. 3, pp. 760-770, Mar. 2003.
17. L. Daudet, S. Molla, and B. Torrésani, "Towards a hybrid audio coder," in Proc. Int. Conf. Wavelet Anal. Applicat., J. P. Li, Ed., Chongqing, China, 2004, pp. 13-24.
18. M. Kowalski, Audio files for the numerical results. Online. Available: http://www.cmi.univ-mrs.fr/~kowalski/IEEE07.html
19. P. Comon, "Independent component analysis, A new concept?," Signal Process., vol. 36, Special Issue on Higher-Order Statistics, no. 3, pp. 287-314, Apr. 1994.
20. D. L. Donoho, "De-noising by soft-thresholding," IEEE Trans. Inf. Theor., vol. 41, no. 3, pp. 613-627, May 1995.
21. J. Stoer and R. Burlish, Introduction to Numerical Analysis. New York: Springer-Verlag, 1991.