Beta-Divergence as a Subclass of Bregman Divergence, IEEE Signal Processing Letters, vol.18, issue.2, pp.83-86, 2011. ,
DOI : 10.1109/LSP.2010.2096211
URL : https://hal.archives-ouvertes.fr/hal-00945202
NMF With Time–Frequency Activations to Model Nonstationary Audio Events, IEEE Transactions on Audio, Speech, and Language Processing, vol.19, issue.4, pp.744-753, 2011. ,
DOI : 10.1109/TASL.2010.2062506
NMF with time-frequency activations to model non stationary audio events, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing ,
DOI : 10.1109/ICASSP.2010.5495733
URL : https://hal.archives-ouvertes.fr/hal-00945293
Spectral similarity measure invariant to pitch shifting and amplitude scaling, Congrès Français d'Acoustique, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00551177
Time-dependent parametric and harmonic templates in non-negative matrix factorization, International Conference On Digital Audio Effects, pp.246-253, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00945292
Scale-invariant probabilistic latent component analysis, 2011 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), 2011. ,
DOI : 10.1109/ASPAA.2011.6082265
URL : https://hal.archives-ouvertes.fr/hal-00960765
Score informed audio source separation using a parametric model of non-negative spectrogram, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) ,
DOI : 10.1109/ICASSP.2011.5946324
URL : https://hal.archives-ouvertes.fr/hal-00945294
Scale-invariant probabilistic latent component analysis. Rapport technique, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00960765
Plumbley : Unsupervised analysis of polyphonic music by sparse coding, IEEE Transactions on neural Networks, vol.17, issue.1, pp.179-196, 2006. ,
Music genre estimation from low level audio features, Audio Engineering Society Conference, 2004. ,
Stability Analysis of Multiplicative Update Algorithms and Application to Nonnegative Matrix Factorization, IEEE Transactions on Neural Networks, vol.21, issue.12, pp.1869-1881, 2010. ,
DOI : 10.1109/TNN.2010.2076831
URL : https://hal.archives-ouvertes.fr/inria-00555984
Weighted maximum likelihood autoregressive and moving average spectrum modeling, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.3761-3764, 2008. ,
DOI : 10.1109/ICASSP.2008.4518471
URL : https://hal.archives-ouvertes.fr/hal-00945273
Expectation-maximization algorithm for multi-pitch estimation and separation of overlapping harmonic spectra, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.3073-3076, 2009. ,
DOI : 10.1109/ICASSP.2009.4960273
URL : https://hal.archives-ouvertes.fr/inria-00452607
Automatic Piano Transcription Using Frequency and Time-Domain Information, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.6, pp.2242-2251, 2006. ,
DOI : 10.1109/TASL.2006.872609
Email surveillance using nonnegative matrix factorization, Computational and Mathematical Organization Theory, vol.11, issue.3, pp.249-264, 2005. ,
Les factorisations en matrices non-négatives. Approches contraintes et probabilistes, application à la transcription automatique de musique polyphonique, Thèse de doctorat, 2009. ,
Blind Signal Decompositions for Automatic Transcription of Polyphonic Music: NMF and K-SVD on the Benchmark, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '07, pp.65-68, 2007. ,
DOI : 10.1109/ICASSP.2007.366617
URL : https://hal.archives-ouvertes.fr/hal-00945282
Enforcing Harmonicity and Smoothness in Bayesian Non-Negative Matrix Factorization Applied to Polyphonic Music Transcription, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.3, pp.538-549, 2010. ,
DOI : 10.1109/TASL.2010.2041381
URL : https://hal.archives-ouvertes.fr/inria-00557088
spectral transform, The Journal of the Acoustical Society of America, vol.89, issue.1, pp.425-434, 1991. ,
DOI : 10.1121/1.400476
Blind signal separation: statistical principles, Proceedings of the IEEE, pp.2009-2025, 1998. ,
DOI : 10.1109/5.720250
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.10.7237
Atomic Decomposition by Basis Pursuit, SIAM Journal on Scientific Computing, vol.20, issue.1, pp.33-61, 1998. ,
DOI : 10.1137/S1064827596304010
Optimality, computation , and interpretation of nonnegative matrix factorizations. Rapport non publié, disponible à l'adresse http, 2004. ,
Extended SMART Algorithms for Non-negative Matrix Factorization, International Conference on Artificial Intelligence and Soft Computing, pp.548-562, 2006. ,
DOI : 10.1007/11785231_58
Csiszar's divergences for nonnegative matrix factorization : Family of new algorithms, Conference on Independent Component Analysis and Blind Source Separation (ICA), pp.32-39, 2006. ,
Plemmons et Shun-Ichi Amari : Non-negative tensor factorization using alpha and beta divergences, IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.1393-1396, 2007. ,
DOI : 10.1109/icassp.2007.367106
New algorithms for nonnegative matrix factorization in applications to blind source separation, International Conference on Acoustics, Speech, and Signal Processing, pp.621-625, 2006. ,
Anh Huy Phan et Shun-Ichi Amari : Nonnegative Matrix and Tensor Factorizations : Applications to Exploratory Multi-way Data Analysis and Blind Source Separation, 2009. ,
Nonnegative ranks, decompositions, and factorizations of nonnegative matrices, Linear Algebra and its Applications, vol.190, pp.149-168, 1993. ,
DOI : 10.1016/0024-3795(93)90224-C
Independent component analysis, A new concept?, Signal Processing, vol.36, issue.3, pp.287-314, 1994. ,
DOI : 10.1016/0165-1684(94)90029-9
URL : https://hal.archives-ouvertes.fr/hal-00417283
Realtime Audio to Score Alignment for Polyphonic Music Instruments, using Sparse Non-Negative Constraints and Hierarchical HMMS, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, 2006. ,
DOI : 10.1109/ICASSP.2006.1661258
URL : https://hal.archives-ouvertes.fr/hal-00723224
Polyphonic audio matching for score following and intelligent audio editors, International Computer Music Conference, pp.27-34, 2003. ,
Generalized nonnegative matrix approximations with Bregman divergences, éditeurs : Neural Information Processing Systems conference (NIPS), pp.283-290, 2006. ,
An amplitude and frequency modulation vocoder for audio signal processing, Conference on Digital Audio Effects (DAFx), pp.257-263, 2008. ,
Multiband perceptual modulation analysis, processing and synthesis of audio signals, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, 2009. ,
DOI : 10.1109/ICASSP.2009.4960081
When does non-negative matrix factorization give a correct decomposition into parts ?, éditeurs : Advances in Neural Information Processing Systems, 2004. ,
A musically motivated mid-level representation for pitch estimation and musical audio source separation. Selected Topics in Signal Processing, IEEE Journal, issue.99, pp.1-2011 ,
Main instrument separation from stereophonic audio signals using a source/filter model, European Signal Processing Conference (EUSIPCO), pp.15-19, 2009. ,
Singer melody extraction in polyphonic signals using source separation methods, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.169-172, 2008. ,
DOI : 10.1109/ICASSP.2008.4517573
An iterative approach to monaural musical mixture de-soloing, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.105-108, 2009. ,
DOI : 10.1109/ICASSP.2009.4959531
Source/Filter Model for Unsupervised Main Melody Extraction From Polyphonic Audio Signals, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.3, pp.564-575, 2010. ,
DOI : 10.1109/TASL.2010.2041114
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.364.2381
Robustifying maximum likelihood estimation, Institute of Statistical Mathematics, 2001. ,
Multipitch Estimation of Piano Sounds Using a New Probabilistic Spectral Smoothness Principle, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.6, pp.1643-1654, 2010. ,
DOI : 10.1109/TASL.2009.2038819
URL : https://hal.archives-ouvertes.fr/inria-00510392
Classification automatique des signaux audio-fréquences : reconnaissance des instruments de musique, Thèse de doctorat, 2006. ,
A spectral-filtering approach to music signal separation, International Conference on Digital Audio Effects, pp.197-200, 2004. ,
Hero : Space-alternating generalized expectationmaximization algorithm, IEEE Transactions on Signal Processing, vol.42, issue.10, pp.2664-2677, 1994. ,
Non-negative tensor factorisation for sound source separation, IEE Irish Signals and Systems Conference 2005, 2005. ,
DOI : 10.1049/cp:20050279
Shifted non-negative matrix factorisation for sound source separation, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, pp.1132-1137, 2005. ,
DOI : 10.1109/SSP.2005.1628765
Phase Vocoder, Bell System Technical Journal, vol.45, issue.9, pp.1493-1509, 1966. ,
DOI : 10.1002/j.1538-7305.1966.tb01706.x
Adaptive harmonic time-frequency decomposition of audio using shift-invariant PLCA, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011. ,
DOI : 10.1109/ICASSP.2011.5946425
Nonnegative Matrix Factorization with the Itakura-Saito Divergence: With Application to Music Analysis, Neural Computation, vol.14, issue.3, pp.793-830, 2009. ,
DOI : 10.1016/j.sigpro.2007.01.024
Algorithms for Nonnegative Matrix Factorization with the ??-Divergence, Neural Computation, vol.11, issue.9, pp.2421-2456 ,
DOI : 10.1109/TASL.2009.2034186
Evaluation of a score-informed source separation system, International Society for Music Information Retrieval Conference ,
Source separation by score synthesis, International Computer Music Conference, 2010. ,
Application of non-negative matrix factorization to fluorescence spectroscopy, European Signal Processing Conference (EU- SIPCO), 2004. ,
Harmonic decomposition of audio signals with matching pursuit, IEEE Transactions on Signal Processing, vol.51, issue.1, pp.101-111, 2003. ,
DOI : 10.1109/TSP.2002.806592
URL : https://hal.archives-ouvertes.fr/inria-00576203
Analysis of a complex of statistical variables into principal components, Journal of Educational Psychology, vol.24, issue.6, pp.471-441, 1933. ,
Non-negative matrix factorization with sparseness constraints, Journal of Machine Learning Research, vol.5, pp.1457-1469, 2004. ,
Analysis synthesis telephony based on the maximum likelihood method, 6th International Congress on Acoustics, pp.17-20, 1968. ,
A Conditional Random Field Framework for Robust and Scalable Audio-to-Score Matching, IEEE Transactions on Audio, Speech, and Language Processing, vol.19, issue.8, pp.2385-2397, 2011. ,
DOI : 10.1109/TASL.2011.2134092
A Generalized Divergence Measure for Nonnegative Matrix Factorization, Neural Computation, vol.39, issue.3, pp.780-791, 2007. ,
DOI : 10.1162/089976602320264033
Leibler : On information and sufficiency. The Annals of Mathematical Statistics, pp.79-86, 1951. ,
DOI : 10.1214/aoms/1177729694
Adaptive template matching with shift-invariant semi-NMF, Daphne Koller, Dale Schuurmans, Yoshua Bengio et Léon Bottou, éditeurs : NIPS, pp.921-928, 2008. ,
Alain de Cheveigné et Shigeki Sagayama : Computational auditory induction by missing-data non-negative matrix factorization, ITRW on Statistical and Perceptual Audio Processing, 2008. ,
Fast signal reconstruction from magnitude STFT spectrogram based on spectrogram consistency, Proc. 13th International Conference on Digital Audio Effects (DAFx-10), pp.397-403, 2010. ,
Learning the parts of objects by non-negative matrix factorization, Nature, vol.401, issue.6755, pp.788-791, 1999. ,
Algorithms for non-negative matrix factorization, éditeur : Advances in Neural Information Processing Systems, pp.556-562, 2000. ,
Décompositions parcimonieuses structurées : application à la représentation objet de la musique, Thèse de doctorat, 2007. ,
Instrument-Specific Harmonic Atoms for Mid-Level Music Representation, IEEE Transactions on Audio, Speech, and Language Processing, vol.16, issue.1, pp.116-128, 2008. ,
DOI : 10.1109/TASL.2007.910786
URL : https://hal.archives-ouvertes.fr/inria-00544175
Projected gradient methods for non-negative matrix factorization, 2007. ,
DOI : 10.1162/neco.2007.19.10.2756
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.9135
Audio source separation based on independent component analysis, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512), pp.668-671, 2004. ,
DOI : 10.1109/ISCAS.2004.1329896
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.652.7569
Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, vol.41, issue.12, pp.3397-3415, 1993. ,
DOI : 10.1109/78.258082
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.335.5769
Pitch-synchronous waveform processing techniques for text-to-speech synthesis using diphones, Speech Communication, vol.9, issue.5-6, pp.453-467, 1990. ,
DOI : 10.1016/0167-6393(90)90021-Z
Non-parametric techniques for pitch-scale and time-scale modification of speech, Speech Communication, vol.16, issue.2, pp.175-205, 1995. ,
DOI : 10.1016/0167-6393(94)00054-E
Relative pitch estimation of multiple instruments, International Conference on Acoustics, Speech and Signal Processing, pp.313-316, 2009. ,
Non-negative hidden Markov modeling of audio with application to source separation, Latent Variable Analysis and Signal Separation, 2010. ,
Nobutaka Ono et Shigeki Sagayama : Convergence-guaranteed multiplicative algorithms for nonnegative matrix factorization with beta-divergence, IEEE International Workshop on Machine Learning for Signal Processing, 2010. ,
Nonnegative Matrix Factorization with Markov-Chained Bases for Modeling Time-Varying Patterns in Music Spectrograms, Latent Variable Analysis and Signal Separation, 2010. ,
DOI : 10.1007/978-3-642-15995-4_19
Infinite-state spectrum model for music signal analysis, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.1972-1975, 2011. ,
DOI : 10.1109/ICASSP.2011.5946896
Chord Recognition by Fitting Rescaled Chroma Vectors to Chord Templates, IEEE Transactions on Audio, Speech, and Language Processing, vol.19, issue.7, pp.2222-2233, 2009. ,
DOI : 10.1109/TASL.2011.2139205
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.417.9058
Multichannel Nonnegative Matrix Factorization in Convolutive Mixtures for Audio Source Separation, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.3, pp.550-563, 2010. ,
DOI : 10.1109/TASL.2009.2031510
Factorial Scaled Hidden Markov Model for polyphonic audio representation and source separation, 2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2009. ,
DOI : 10.1109/ASPAA.2009.5346527
URL : https://hal.archives-ouvertes.fr/inria-00553336
Positive matrix factorization: A non-negative factor model with optimal utilization of error estimates of data values, Environmetrics, vol.18, issue.2, pp.111-126, 1994. ,
DOI : 10.1002/env.3170050203
Informed source separation of underdetermined instantaneous stereo mixtures using source index embedding, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.1721-1733, 2011. ,
DOI : 10.1109/ICASSP.2010.5495983
URL : https://hal.archives-ouvertes.fr/hal-00486804
A Watermarking-Based Method for Informed Source Separation of Audio Signals With a Single Sensor, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.6, pp.1464-1475, 2010. ,
DOI : 10.1109/TASL.2009.2035216
URL : https://hal.archives-ouvertes.fr/hal-00486809
Plemmons : Text mining using non-negative matrix factorizations, SIAM international conference on data mining, pp.452-456, 2004. ,
DOI : 10.1137/1.9781611972740.45
Drum transcription with non-negative spectrogram factorization, European Signal Processing Conference (EUSIPCO), 2005. ,
Aligning music audio with symbolic scores using a hybrid graphical model, Machine Learning, vol.65, issue.2-3, pp.389-409, 2006. ,
DOI : 10.1007/s10994-006-8415-3
A Classifier-Based Approach to Score-Guided Source Separation of Musical Audio, Computer Music Journal, vol.17, issue.1, pp.51-59, 2008. ,
DOI : 10.1109/TSA.2005.860342
A parametric model of piano tuning, International Conference On Digital Audio Effects, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00727395
Tempo and beat analysis of acoustic musical signals, The Journal of the Acoustical Society of America, vol.103, issue.1, pp.588-601, 1998. ,
DOI : 10.1121/1.421129
Nonnegative matrix factorization with gaussian process priors, Computational Intelligence and Neuroscience, pp.1-10, 2008. ,
Nonnegative matrix factor 2-D deconvolution for blind single channel source separation, Conference on Independent Component Analysis and Blind Source Separation (ICA), volume 3889 de Lecture Notes in Computer Science (LNCS), pp.700-707, 2006. ,
Constant-Q transform toolbox for music processing, 7th Sound and Music Computing Conference, 2010. ,
Raj et Paris Smaragdis : Sparse overcomplete latent variable decomposition of counts data, Neural Information Processing Systems, 2007. ,
Probabilistic latent variable models as non-negative factorizations. in special issue on advances in non-negative matrix and tensor factorization. special issue on Advances in Non-negative Matrix and Tensor Factorization, Computational Intelligence and Neuroscience Journal, p.947438, 2008. ,
Non-negative Matrix Factor Deconvolution; Extraction of Multiple Sound Sources from Monophonic Inputs, Conference on Independent Component Analysis and Blind Source Separation (ICA), pp.494-499, 2004. ,
DOI : 10.1007/978-3-540-30110-3_63
Non-negative matrix factorization for polyphonic music transcription, 2003 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (IEEE Cat. No.03TH8684), pp.177-180, 2003. ,
DOI : 10.1109/ASPAA.2003.1285860
Separation by “humming”: User-guided sound extraction from monophonic mixtures, 2009 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, pp.69-72, 2009. ,
DOI : 10.1109/ASPAA.2009.5346542
Supervised and semisupervised separation of sounds from single-channel mixtures, 7th International Conference on Independent Component Analysis and Signal Separation, 2007. ,
Sparse and shift-invariant feature extraction from non-negative data, 2008 IEEE International Conference on Acoustics, Speech and Signal Processing, pp.2069-2072, 2008. ,
DOI : 10.1109/ICASSP.2008.4518048
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.3967
Missing data imputation for spectral audio signals, 2009 IEEE International Workshop on Machine Learning for Signal Processing, 2009. ,
DOI : 10.1109/MLSP.2009.5306194
Missing Data Imputation for Time-Frequency Representations of Audio Signals, Journal of Signal Processing Systems, vol.32, issue.2, 2010. ,
DOI : 10.1007/s11265-010-0512-7
Latent Dirichlet decomposition for single channel speaker separation, IEEE International Conference on Acoustics, Speech, and Signal Processing, 2006. ,
Adaptive Harmonic Spectral Decomposition for Multiple Pitch Estimation, IEEE Transactions on Audio, Speech, and Language Processing, vol.18, issue.3, pp.528-537, 2010. ,
DOI : 10.1109/TASL.2009.2034186
URL : https://hal.archives-ouvertes.fr/inria-00544094
Performance measurement in blind audio source separation, IEEE Transactions on Audio, Speech and Language Processing, vol.14, issue.4, pp.1462-1469, 2006. ,
DOI : 10.1109/TSA.2005.858005
URL : https://hal.archives-ouvertes.fr/inria-00544230
Monaural Sound Source Separation by Nonnegative Matrix Factorization With Temporal Continuity and Sparseness Criteria, IEEE Transactions on Audio, Speech and Language Processing, vol.15, issue.3, pp.1066-1074, 2007. ,
DOI : 10.1109/TASL.2006.885253
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.330.1508
Bayesian extensions to nonnegative matrix factorisation for audio signal modelling, IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.1825-1828, 2008. ,
DOI : 10.1109/icassp.2008.4517987
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.401.4325
Automatic generation of lead sheets from polyphonic music signals, International Society for Music Information Retrieval Conference, 2009. ,
Remixing stereo music with score-informed source separation, International Conference on Music Information Retrieval, 2006. ,
Nonnegative matrix factorization with constrained second-order optimization, Signal Processing, vol.87, issue.8, pp.1904-1916, 2007. ,
DOI : 10.1016/j.sigpro.2007.01.024
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.63.5201
A NMF algorithm for blind separation of uncorrelated signals11 Décomposition invariante par translation temporelle du spectrogramme V (en-bas à droite) contenant des éléments percussifs (boucle de batterie) U 1 , U 2 et U 3 (en-bas à gauche) sont les trois atomes temps/fréquence, correspondant chacun à un élément de batterie (respectivement, grosse caisse, charleston et caisse claire) Les activations H (en-haut à droite) doivent être très parcimonieuses pour que la décomposition ait de l'intérêt : ici les activations prennent effectivement une forme très, International Conference on Wavelet Analysis and Pattern Recognition, pp.999-1003, 2007. ,
et P = 1) du spectrogramme de puissance de l'extrait de clavecin, p.73 ,
Spectrogramme original de l'extrait du premier prélude ,
une Transformée de Fourier à Court Terme (TFCT)) des premières notes d'Au clair de la lune jouées par un synthétiseur . Illustration de l'équivalence homothétie/transposition dans un tel spectrogramme (le motif translaté ne s'adapte pas correctement), p.99 ,
Distribution d'impulsions P I de l'introduction, p.109 ,
7(a) original et des spectrogrammes modèles 5.7(b) (total), 5.7(c) (note isolée) et 5.7(d) (reste) de l'introduction, Zoom sur les basses fréquences des premières secondes du spectrogramme 5, p.126 ,
qui ont su m'orienter intelligemment et m'accompagner dans mon travail en faisant preuve d'une grande disponibilité malgré des emplois du temps souvent surchargés : Bertrand pour son optimisme permanent et Roland pour sa grande rigueur scientifique. Je remercie l'ensemble des membres du jury pour l'intérêt qu'ils ont porté à mes travaux, Remerciements Je tiens à remercier avant tout mes directeurs de thèse ,
leur compétence et leur sérieux qui ont permis de réaliser cette thèse dans d'excellentes conditions Un grand merci également au personnel administratif de TÉLÉ- COM ParisTech qui fait un excellent travail toujours dans la bonne humeur, en particulier Laurence Zelmar, Je remercie toute les membres présents et passés de l'équipe Audiosig de TÉLÉCOM ParisTech pour leur bonne humeur grand merci à tous les membres de ma famille pour leur soutien : ma mère Patricia, mon père Bernard, ma soeur Laura, mon grand-père Paul-Louis ainsi qu'à ma grand-mère Marinette qui nous a malheureusement quitté pendant cette thèse ,
Samer quoi !) Je remercie également tous les ATIAM de ma promotion, Léni et Sophie, La Pompe et Samer qui me supporte depuis maintenant plus de cinq ans, pour ses nombreuses et vaines tentatives de comprendre le sujet de ma thèse mais surtout pour son soutien et son réconfort sans faille ,