Sparse atomic modeling of audio: A review

Proceedings of the International Conference on Digital Audio Effects, DAFx

Volumn , Issue , 2011, Pages 81-92

  Kereliuk, Corey ^a   Depalle, Philippe ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; ATOMS; BAYESIAN NETWORKS; LEAST SQUARES APPROXIMATIONS;

APPROXIMATION PROBLEMS; ATOMIC MODELS; AUDIO APPLICATIONS; AUDIO PROCESSING; GREEDY ALGORITHMS; IMAGES PROCESSING; ITERATIVE SHRINKAGES; RE-WEIGHTED LEAST-SQUARES; SPARSE APPROXIMATIONS; STATE OF THE ART;

ITERATIVE METHODS;

EID: 84872717682     PISSN: 24136700     EISSN: 24136689     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (72)

1. M. Elad, P. Milanfar, and R. Rubinstein, "Analysis versus synthesis in signal priors," Inverse Problems, vol. 23, pp. 947-968, 2007.
2. S. Nam, M. Davies, M. Elad, and R. Gribonval, "Cosparse analysis modeling-uniqueness and algorithms," Proc. Int. Conf. Acoust. Speech Sig. Proc., 2011.
3. I. Daubechies, A. Grossmann, and Y. Meyer, "Painless nonorthogonal expansions," J. Math. Phys, vol. 27, no. 5, pp. 1271-1283, 1986.
4. J. Kovacevic and A. Chebira, "Life Beyond Bases: The Advent of Frames (Part I)," IEEE Sig. Proc. Mag., vol. 24, no. 4, pp. 86-104, July 2007.
5. M. Goodwin, "Matching pursuit with damped sinusoids," in Proc. Int. Conf. Acoust. Speech Signal Process, 1997, vol. 3, pp. 2037-2040.
6. G. Davis, S. Mallat, and Z. Zhang, "Adaptive time-frequency decompositions with matching pursuit," in Proc. of SPIE, 1994, vol. 2242, pp. 402-413.
7. J.A. Tropp, "Greed is good: Algorithmic results for sparse approximation," IEEE Transactions on Information Theory, vol. 50, no. 10, pp. 2231-2242, 2004.
8. J.A. Tropp, "Just relax: Convex programming methods for identifying sparse signals in noise," IEEE Trans. on Inf. Theory, vol. 52, no. 3, pp. 1030-1051, 2006.
9. S.G. Mallat and Z. Zhang, "Matching pursuits with time-frequency dictionaries," IEEE Trans. on Sig. Proc., vol. 41, no. 12, pp. 3397-3415, 1993.
10. B. Mailhé, R. Gribonval, P. Vandergheynst, and F. Bimbot, "Fast orthogonal sparse approximation algorithms over local dictionaries," Signal Processing, 2011.
11. R. Heusdens, R. Vafin, and W.B. Kleijn, "Sinusoidal modeling using psychoacoustic-adaptive matching pursuits," Signal Processing Letters, IEEE, vol. 9, no. 8, pp. 262-265, 2002.
12. R. Gribonval, E. Bacry, S. Mallat, P. Depalle, and X. Rodet, "Analysis of sound signals with high resolution matching pursuit," in Proc. of the IEEE Int. Sym. on Time-Freq. and Time-Scale Analysis, 1996, pp. 125-128.
13. P. Leveau and L. Daudet, "Multi-resolution partial tracking with modified matching pursuit," in Proc. Eur. Signal Process. Conf., 2006.
14. M.G. Christensen and S.H. Jensen, "The cyclic matching pursuit and its application to audio modeling and coding," in Signals, Systems and Computers, 2007. ACSSC 2007. Conference Record of the Forty-First Asilomar Conference on. IEEE, 2007, pp. 550-554.
15. Y.C. Pati, R. Rezaiifar, and P.S. Krishnaprasad, "Orthogonal matching pursuit: recursive function approximation with applications to wavelet decomposition," Asilomar Conf. on Sig., Sys. and Comp., vol. 1, pp. 40-44, 1993.
16. L. Rebollo-Neira and D. Lowe, "Optimized orthogonal matching pursuit approach," Signal Processing Letters, IEEE, vol. 9, no. 4, pp. 137-140, 2002.
17. David L. Donoho, Yaakov Tsaig, Iddo Drori, and Jean-Luc Starck, "Sparse Solution of Underdetermined Linear Equations by Stagewise Orthogonal Matching Pursuit," Tech. Rep., Stanford, 2006.
18. T. Blumensath and M.E. Davies, "Gradient pursuits," IEEE Trans. on Sig. Proc., vol. 56, no. 6, pp. 2370-2382, 2008.
19. M. Goodwin, Handbook of Speech Processing, chapter 12, pp. 229-258, Springer-Verlag, Berlin, 2008.
20. R. Gribonval and M. Nielsen, "Approximate weak greedy algorithms," Adv. in Comp. Math., vol. 14, no. 4, pp. 361-378, 2001.
21. V.N. Temlyakov, "Weak greedy algorithms," Adv. in Comp. Math., vol. 12, no. 2-3, pp. 213-227, 2000.
22. F. Bergeaud and S. Mallat, "Matching pursuit: Adaptive representations of images and sounds," Comp. and Applied Math., vol. 15, pp. 97-110, 1996.
23. R. Gribonval and E. Bacry, "Harmonic decomposition of audio signals with matching pursuit," IEEE Trans. on Sig. Proc., vol. 51, no. 1, pp. 101-111, 2003.
24. R.R. Coifman and M.V.Wickerhauser, "Entropy-based algorithms for best basis selection," IEEE Trans. on Inf. Theory, vol. 38, no. 2, pp. 713-718, 1992.
25. F. Jaillet and B. Torrésani, "Time-Frequency Jigsaw Puzzle: adaptive multiwindow and multilayered Gabor expansions," Int. J. Wavelets, Multires. and Inf. Proc., vol. 5, no. 2, pp. 293-315, 2007.
26. J.F. Claerbout and F. Muir, "Robust modeling with erratic data," Geophysics, vol. 38, pp. 826, 1973.
27. S.S. Chen, D.L. Donoho, and M.A. Saunders, "Atomic decomposition by basis pursuit," SIAM review, vol. 43, no. 1, pp. 129-159, 2001.
28. R. Tibshirani, "Regression shrinkage and selection via the LASSO," J. Royal Stat. Soc., pp. 267-288, 1996.
29. S.P. Boyd and L. Vandenberghe, Convex optimization, Cambridge University Press, 2004.
30. M.G. Christensen and S.H. Jensen, "On compressed sensing and its application to speech and audio signals," in Signals, Systems and Computers, 2009 Conference Record of the Forty-Third Asilomar Conference on. IEEE, 2009, pp. 356-360.
31. D.L. Donoho, "Compressed sensing," Information Theory, IEEE Transactions on, vol. 52, no. 4, pp. 1289-1306, 2006.
32. B.D. Rao and K. Kreutz-Delgado, "An affine scaling methodology for best basis selection," IEEE Trans. on Sig. Proc., vol. 47, no. 1, pp. 187-200, 1999.
33. I.F. Gorodnitsky and B.D. Rao, "Sparse signal reconstruction from limited data using FOCUSS: A Re-weighted minimum norm algorithm," IEEE Trans. on Sig. Proc., vol. 45, no. 3, pp. 600-616, 1997.
34. I. Daubechies, R. DeVore, M. Fornasier, and S. Gunturk, "Iteratively re-weighted least squares minimization for sparse recovery," Commun. Pure Appl. Math, vol. 63, no. 1, pp. 1-38, 2009.
35. Z. He, A. Cichocki, R. Zdunek, and S. Xie, "Improved FOCUSS method with conjugate gradient iterations," IEEE Trans. on Sig. Proc., vol. 57, no. 1, pp. 399-404, 2009.
36. M.E. Davies and L. Daudet, "Sparse audio representations using the MCLT," Signal processing, vol. 86, no. 3, pp. 457-470, 2006.
37. S. Sardy, A.G. Bruce, and P. Tseng, "Block coordinate relaxation methods for nonparametric signal denoising with wavelet dictionaries," Journal of computational and graphical statistics, vol. 9, pp. 361-379, 2000.
38. D.L. Donoho and J.M. Johnstone, "Ideal spatial adaptation by wavelet shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, 1994.
39. M. Kowalski, "Sparse regression using mixed norms," Applied and Computational Harmonic Analysis, vol. 27, no. 3, pp. 303-324, 2009.
40. T. Blumensath, M. Yaghoobi, and M.E. Davies, "Iterative hard thresholding and l0 regularisation," in Proc. Int. Conf. Acoust. Speech Sig. Proc., 2007.
41. M.A.T. Figueiredo and R.D. Nowak, "An EM algorithm for wavelet-based image restoration," IEEE Trans. on Image Proc., vol. 12, no. 8, pp. 906-916, 2003.
42. I. Daubechies, M. Defrise, and C. De Mol, "An iterative thresholding algorithm for linear inverse problems with a sparsity constraint," Commun. Pure Appl. Math, vol. 57, no. 11, pp. 1413-1457, 2004.
43. M. Elad, "Why simple shrinkage is still relevant for redundant representations?," IEEE Trans. on Inf. Theory, vol. 52, no. 12, pp. 5559-5569, 2006.
44. K.K. Herrity, A.C. Gilbert, and J.A. Tropp, "Sparse approximation via iterative thresholding," in Proc. Int. Conf. Acoust. Speech Signal Proc., 2006, vol. 3, pp. 624-627.
45. J.M. Bioucas-Dias and M.A.T. Figueiredo, "A new twist: two-step iterative shrinkage/thresholding algorithms for image restoration," Image Processing, IEEE Transactions on, vol. 16, no. 12, pp. 2992-3004, 2007.
46. A. Beck and M. Teboulle, "A fast iterative shrinkage-thresholding algorithm for linear inverse problems," SIAM Journal on Imaging Sciences, vol. 2, no. 1, pp. 183-202, 2009.
47. M.S. Lewicki and T.J. Sejnowski, "Learning overcomplete representations," Neural computation, vol. 12, no. 2, pp. 337-365, 2000.
48. R. Gribonval, "Should penalized least squares regression be interpreted as Maximum A Posteriori estimation?," IEEE Transactions on Signal Processing, vol. 59, no. 5, pp. 2405-2410, May 2011.
49. M.D. Plumbley, S.A. Abdallah, T. Blumensath, and M.E. Davies, "Sparse representations of polyphonic music," Signal Processing, vol. 86, no. 3, pp. 417-431, 2006.
50. K. Kreutz-Delgado, J.F. Murray, B.D. Rao, K. Engan, T.W. Lee, and T.J. Sejnowski, "Dictionary learning algorithms for sparse representation," Neural Computation, vol. 15, no. 2, pp. 349-396, 2003.
51. D.P.Wipf and B.D. Rao, "Sparse Bayesian learning for basis selection," IEEE Trans. on Sig. Proc., vol. 52, no. 8, pp. 2153-2164, 2004.
52. M.E. Tipping, "Sparse Bayesian learning and the relevance vector machine," J. Mach. Learn. Res., vol. 1, pp. 211-244, 2001.
53. M.A.T. Figueiredo, "Adaptive sparseness for supervised learning," IEEE Trans. Pattern Anal. Mach. Intell., vol. 25, no. 9, pp. 1150-1159, 2003.
54. 0 norm," IEEE Trans. on Sig. Proc., vol. 57, pp. 289-301, 2009.
55. P.J. Wolfe, S.J. Godsill, and W.J. Ng, "Bayesian variable selection and regularization for time-frequency surface estimation," J. Royal Stat. Soc., vol. 66, no. 3, pp. 575-589, 2004.
56. C. Fevotte and S.J. Godsill, "Sparse linear regression in unions of bases via Bayesian variable selection," IEEE Sig. Proc. Let., vol. 13, pp. 441-444, 2006.
57. E.I. George and R.E. McCulloch, "Approaches for Bayesian variable selection," Statistica Sinica, vol. 7, pp. 339-374, 1997.
58. C. Fevotte, B. Torresani, L. Daudet, and S.J. Godsill, "Sparse linear regression with structured priors and application to denoising of musical audio," IEEE Trans. Audio, Speech, Lang. Proc., vol. 16, no. 1, pp. 174-185, 2008.
59. R. Gribonval, "Sparse decomposition of stereo signals with matching pursuit and application to blind source separation of more than two sources from a stereo mixture," in Proc. Int. Conf. Acoust. Speech Signal Proc., 2002, vol. 3, pp. 3057-3060.
60. L. Daudet, "Sparse and structured decompositions of signals with the molecular matching pursuit," IEEE Trans. Audio, Speech, Lang. Proc., vol. 14, no. 5, pp. 1808-1816, 2006.
61. X. Serra and J.O. Smith, "Spectral modeling synthesis: a sound analysis/synthesis system based on a deterministic plus stochastic decomposition," Computer Music Journal, vol. 14, no. 4, pp. 12-24, 1990.
62. P. Depalle, G. Garcia, and X. Rodet, "Tracking of partials for additive sound synthesis using hidden Markov models," in Proc. Int. Conf. Acoust. Speech Sig. Proc., 1993, vol. 1, pp. 242-245.
63. P. Leveau, E. Vincent, G. Richard, and L. Daudet, "Instrument- specific harmonic atoms for mid-level music representation," IEEE Transactions on Audio Speech and Language Processing, vol. 16, no. 1, pp. 116-128, 2008.
64. B.L. Sturm, J.J. Shynk, and S. Gauglitz, "Agglomerative clustering in sparse atomic decompositions of audio signals," in Proc. Int. Conf. Acoust. Speech Signal Proc., 2008, pp. 97-100.
65. M. Kowalski and B. Torrésani, "Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients," Sig., Image and Video Proc., vol. 3, no. 3, pp. 251-264, 2009.
66. D. Donoho, "Sparselab website," 2011, http://sparselab. stanford.edu/.
67. T. Blumensath, "Sparsify website," 2011, http://users.fmrib.ox. ac.uk/~tblumens/sparsify/sparsify.html.
68. S. Krstulovic and R. Gribonval, "MPTK: Matching Pursuit made tractable," in Proc. Int. Conf. Acoust. Speech Signal Proc., 2006, vol. 3, pp. 496-499.
69. C. Kereliuk, "Gablab website and supplementary materials," 2011, http://www.music.mcgill.ca/~corey/dafx2011.
70. B.L. Sturm, C. Roads, A. McLeran, and J.J. Shynk, "Analysis, visualization, and transformation of audio signals using dictionary-based methods," Journal of New Music Research, vol. 38, no. 4, pp. 325-341, 2009.
71. S.G. Mallat, A Wavelet Tour of Signal Processing: The Sparse Way, Academic Press, Burlington, MA, 3rd edition, 2009.
72. A. Adler, V. Emiya, G. Jafari, M. Elad, R. Gribonval, and M.D. Plumbley, "Audio Inpainting," Research report, Mar. 2011.