This paper investigates the use of musical priors for sparse expansion of audio signals of music, on an overcomplete dual-resolution dictionary taken from the union of two orthonormal bases that can describe both transient and tonal components of a music audio signal. More specifically, chord and metrical structure information are used to build a structured model that takes into account dependencies between coefficients of the decomposition, both for the tonal and for the transient layer. The denoising task application is used to provide a proof of concept of the proposed musical priors. Several configurations of the model are analyzed. Evaluation on monophonic and complex polyphonic excerpts of real music signals shows that the proposed approach provides results whose quality measured by the signal-to-noise ratio is competitive with state-of-the-art approaches, and more coherent with the semantic content of the signal. A detailed analysis of the model in terms of sparsity and in terms of interpretability of the representation is also provided and shows that the model is capable of giving a relevant and legible representation of Western tonal music audio signals.
REFERENCES
1.
Baraniuk
, R.
, Flandrin
, P.
, Janssen
, A.
, and Michel
, O.
(2001
). “Measuring time-frequency information content using the Rényi entropies
,” Proc. IEEE Trans. Inf. Theory
47
, 1391
–1409
.2.
Bello
, J.
, and Pickens
, J.
(2005
). “A robust mid-level representation for harmonic content in music signal
,” in Proceedings of the International Symposium on Music Information Retrieval
(International Society for Music Information Retrival, London, UK).3.
Benaroya
, L.
, Bimbot
, F.
, and Gribonval
, R.
(2006
). “Audio source separation with a single sensor
,” IEEE Trans. Audio Speech Language Processing
14
, 191
–199
.4.
Blumensath
, T.
, and Davies
, M.
(2004
). “Unsupervised learning of sparse and shift-invariant decompositions of polyphonic music
,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processings
(ICASSP, Montreal, Canada), Vol. 5
, pp. 497
–500
.5.
Brown
, J.
(1991
). “Calculation of a constant Q spectral transform
,” J. Acoust. Soc. Am.
89
, 425
–434
.6.
Casella
, G.
, and George
, E.
(1992
). “Explaining the Gibbs sampler
,” Am. Stat.
46
, 167
–174
.7.
Chen
, S.
, David L. Donoho
, D.
, and Saunders
, M.
(1998
). “Atomic decomposition by basis pursuit
,” SIAM J. Sci. Comput.
20
, 33
–61
.8.
Crouse
, M.
, Nowak
, R.
, and Baraniuk
, R.
(1998
). “Wavelet-based statistical signal processing using hidden markov models
,” IEEE Trans. Sig. Processing
46
, 886
–902
.9.
Daudet
, L.
(2004
). “Sparse and structured decompositions of audio signals in overcomplete spaces
,” in Proceedings of the International Conference on Digital Audio Effects (DAFx'04)
(Naples, Italy), pp. 22
–26
.10.
Daudet
, L.
(2006a
). “A review on techniques for the extraction of transients in musical signals
,” in Computer Music Modeling and Retrieval, Lecture Notes in Computer Science
(Springer-Verlag
, Berlin
), Vol. 3902
, pp. 219
–232
.11.
Daudet
, L.
(2006b
). “Sparse and structured decompositions of signals with the molecular matching pursuit
,” IEEE Trans. Audio Speech Language Processing
14
, 1808
–1816
.12.
Daudet
, L.
(2010
). “Audio sparse decompositions in parallel, Let the greed be shared!
” IEEE Trans. Signal Processing
27
, 90
–96
.13.
Daudet
, L.
, Molla
, S.
, and Torrésani
, B.
(2004
). “Towards a hybrid audio coder
,” in Proceedings of the International Conference Wavelet Analysis Its Applications
(Chongqing, Chine), pp. 13
–24
.14.
Daudet
, L.
, and Torrésani
, B.
(2002
). “Hybrid representations for audiophonic signal encoding
,” Signal Proc. J.
82
, 1595
–1617
.15.
Daudet
, L.
, and Torrésani
, B.
(2006
). Signal Processing Methods for Music Transcription
(Springer
, New York)
, Chap. 3, pp. 65
–98
.16.
Davies
, M.
, and Daudet
, L.
(2006
). “Sparse audio representations using the MCLT
” Signal Processing J.
86
, 457
–470
.17.
Davies
, M.
, and Plumbley
, M.
(2007
). “Context-dependent beat tracking of musical audio
,” IEEE Trans. Audio Speech Language Processing
15
, 1009
–1020
.18.
Dixon
, S.
(2007
). “Evaluation of audio beat tracking system beatroot
,” J. New Music Res.
36
, 39
–51
.19.
Emiya
, V.
, Vincent
, E.
, Harlander
, N.
, and Hohmann
, V.
(2010
). “Subjective and objective quality assessment of audio source separation
,” IEEE Trans. Audio, Speech, Lang. Process.
19
(7
), 2046
–2057
.20.
Févotte
, C.
, Daudet
, L.
, Godsill
, S.
, and Torresani
, B.
(2006
). “Sparse regression with structured priors: Application to audio denoising
,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processings
(Toulouse, France), Vol. 3
.21.
Févotte
, C.
, and Godsill
, S.
(2006a
). “A Bayesian approach for blind separation of sparse sources
,” IEEE Trans. Audio Speech Language Processing
14
, 2174
–2188
.22.
Févotte
, C.
, and Godsill
, S.
(2006b
). “Sparse linear regression in unions of bases via Bayesian variable selection
” IEEE Signal Processing Letters
13
, 441
–444
.23.
Févotte
, C.
, Torrésani
, B.
, Daudet
, L.
, and Godsill
, S.
(2008
). “Sparse linear regression with structured priors and application to denoising of musical audio
,” IEEE Trans. Audio Speech Language Processing
16
, 174
–185
.24.
Figueiredo
, M.
(2003
). “Adaptive sparseness for supervised learning
,” IEEE Trans. Pattern Anal. Mach. Intell.
25
, 1150
–1159
.25.
Fujishima
, T.
(1999
). “Real-time chord recognition of musical sound: a system using common lisp music
,” in Proceedings of the International Computer Music Conference
(Bejing, China) (MPublishing, Ann Arbor, MI), pp. 464
–467
.26.
Geman
, S.
, and Geman
, D.
(1984
). “Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
,” IEEE Trans. Pattern Anal. Mach. Intell.
6
, 721
–741
.27.
George
, E.
, and McCulloch
, R.
(1997
). “Approaches for Bayesian variable selection.
” Stat. Sin.
7
, 339
–373
.28.
Geweke
, J.
(1996
). “Variable selection and model comparison in regression
,” Bayesian Stat.
5
, 609
–620
.29.
Hamdy
, K.
, Ali
, M.
, and Tewfi
, A.
(1996
). “Low bit rate high quality audio coding with combined harmonic and wavelet representations
,” in Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processings
(Atlanta, GA) (IEEE, Piscataway, NJ), Vol. 2
, pp. 1045
–1048
.30.
Harte
, C.
, and Sandler
, M.
(2005
). “Automatic chord identification using a quantised chromagram
,” in Proceedings of the Convention Audio Engineering Society (AES)
(Barcelona, Spain) (AES, New York).31.
Jaillet
, F.
, and Torrésani
, B.
(2004
). “Time-frequency jigsaw puzzle- Adaptive multiwindow and multilayered gabor expansions
,” technical report (LATP, Université de Provence, Marseille, France).32.
Klapuri
, A.
, Eronen
, A.
, and Astola
, J.
(2006
). “Analysis of the meter of acoustic musical signals
,” IEEE Trans. Audio Speech Language Processing
14
, 342
–355
.33.
Kowalski
, M.
(2009
). “Sparse regression using mixed norms
,” Appl. Comput. Harmonic Anal.
27
, 303
–324
.34.
Kowalski
, M.
, and Torrésani
, B.
(2008
). “Random models for sparse signals expansion on unions of bases with application to audio signals
,” IEEE Trans. Signal Processing
56
, 3468
–3481
.35.
Liuni
, M.
, Roebel
, A.
, Romito
, M.
, and Rodet
, X.
(2011
). “An entropy Based method for Local time-adaptation of the spectrogram
,” in Computer Music Modeling and Retrieval, Lecture Notes in Computer Science
(Springer-Verlag
, Berlin
), pp. 60
–75
.36.
Low
, F.
(1985
). “Complete sets of wave packets
,” in A Passion for Physics—Essay in Honor of Geoffrey Chew
, edited by C.
DeTar
(World Scientific
, New York
), pp. 17
–22
.37.
Mallat
, S.
(1998
). A Wavelet Tour of Signal Processing
, 3rd ed. (Academic Press
, San Diego, CA
), 832
p.38.
Mallat
, S.
, and Zhang
, Z.
(1993
). “Matching pursuit with time-frequency dictionaries
,” IEEE Trans. Signal Processing
41
, 3397
–3415
.39.
Malvar
, H.
(1990
). “Lapped transforms for efficient transform/subband coding
,” IEEE Trans. Acoust. Speech Signal Processing
38
, 969
–978
.40.
Molla
, S.
, and Torrésani
, B.
(2004
). “Determining local transientness of audio signals
,” IEEE Signal Processing Lett.
11
, 625
–628
.41.
Molla
, S.
, and Torrésani
, B.
(2005
). “An hybrid audio scheme using hidden Markov models of waveforms
,” Appl. Comput. Harmonic Anal.
18
, 137
–166
.42.
Noland
, K.
and Sandler
, M.
(2006
). “Key estimation using a hidden Markov model
,” in Proceedings of the International Symposium on Music Information Retrieval
(Victoria, BC, Canada).43.
Papadopoulos
, H.
, and Kowalski
, M.
(2011
). “Sparse Signal Decomposition on Hybrid Dictionaries Using Musical Priors
,” in Proceedings of the International Symposium on Music Information Retrieval
(International Society for Music Information Retrival, Miami, FL).44.
Papadopoulos
, H.
, and Kowalski
, M.
(2012
). “Sound files
,” http://www.lss.supelec.fr/perso/kowalski/jasa/jasa.htm (Last viewed April 9, 2012).45.
Papadopoulos
, H.
, and Peeters
, G.
(2007
). “Large-scale study of chord estimation algorithms based on chroma representation and hmm
,” in Proceedings of the International Workshop on Content-Based Multimedia Indexing (CBMI)
(Bordeaux, France), pp. 53–60.46.
Papadopoulos
, H.
, and Peeters
, G.
(2011
). “Joint estimation of chords and downbeats
,” IEEE Trans. Audio Speech Language Processing
19
, 138
–152
.47.
Pati
, Y.
, Rezaiifar
, R.
, and Krishnaprasad
, P.
(1993
). “Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition
,” in Proceedings of the 27th Annual Asilomar Conference on Signals, Systems, and Computers
(Pacific Grove, CA), pp. 40
–44
.48.
Peeters
, G.
(2006
). “Musical key estimation of audio signal based on HMM modeling of chroma vectors
,” in Proceedings of the International Conference on Digital Audio Effects (DAFx)
(Montreal, Canada), pp. 127
–131
.49.
Peeters
, G.
, and Papadopoulos
, H.
(2011
). “Simultaneous beat and downbeat-tracking using a probabilistic framework: Theory and large-scale evaluation
,” IEEE Trans. Audio Speech Language Processing
19
, 1754
–1769
.50.
Plumbley
, M.
, Blumensath
, T.
, Daudet
, L.
, Gribonval
, R.
, and Davies
, M.
(2010
). “Sparse Representations in audio and music: From coding to source separation
,” Proc. IEEE
98
, 995
–1005
.51.
Ravelli
, E.
, Richard
, G.
, and Daudet
, L.
(2008
). “Union of MDCT bases for audio coding
,” IEEE Trans. Audio Speech Language Processing
16
, 1361
–1372
.52.
Ravelli
, E.
, Richard
, G.
, and Daudet
, L.
(2010
). “Audio signal representations for indexing in the transform domain
,” IEEE Trans. Audio Speech Language Processing
18
, 434
–446
.53.
Rényi
, A.
(1961
). “On measures of entropy and information
,” in Proceedings of the Fourth Berkeley Symposium on Mathematics of Statistics and Probability
(University of California Press
, Berkeley, CA
), Vol. 41
, pp. 547
–561
.54.
Rohdenburg
, T.
, Hohmann
, V.
, and Kollmeier
, B.
(2005
). “Objective perceptual quality measures for the evaluation of noise reduction schemes
,” in Proceedings of the 9th International Workshop on Acoustic Echo and Noise Control
(Technische Universiteit Eindhoven, Eindhoven, The Netherlands), pp. 169–172.55.
Scheirer
, E.
(1998
). “Tempo and beat analysis of acoustic musical signals
,” J. Acoust. Soc. Am.
103
, 588
–601
.56.
Sheh
, A.
, and Ellis
, D.
(2003
). “Chord segmentation and recognition using EM-trained HMM
,” in Proceedings of the International Symposium on Music Information Retrieval
(International Society for Music Information Retrieval, Baltimore, MD).57.
Tibshirani
, R.
(1996
). “Regression shrinkage and selection via the lasso
,” J. R. Stat. Soc. Ser. B
58
, 267
–288
.58.
Verma
, T.
, and Meng
, T.
(2000
). “Extending spectral modeling synthesis with transient modeling synthesis
,” Comput. Music J.
24
, 47
–59
.59.
Vincent
, E.
, Jafari
, M.
, and Plumbley
, M. D.
(2006
). “Preliminary guidelines for subjective evaluation of audio source separation algorithms
,” in Proceedings of the UK ICA Research Network Workshop
(Royaume-Uni, Southampton, UK), pp. 93
–96
.60.
Wakefield
, G.
(1999
). “Mathematical representation of joint time-chroma distribution
,” in Proceedings of the SPIE Conference on Advanced Signal Processing Algorithms, Architecture and Implementation
(ASPAAI, Denver, CO), pp. 637
–645
.61.
Wolfe
, P.
, Godsill
, S.
, and Ng
, W.-J.
(2004
). “Bayesian variable selection and regularization for time-frequency surface estimation
,” J. R. Stat. Soc. Ser. B
66
, 575
–589
.62.
Yeh
, C.
, Roebel
, A.
, and Rodet
, X.
(2010
). “Multiple fundamental frequency estimation and polyphony inference of polyphonic music signals
,” IEEE Trans. Audio Speech Language Processing
18
, 1116
–1126
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