Dans cette thèse, nous nous intéressons au système d’identification automatique spatial lequel est dédié à la surveillancemaritime par satellite. Ce système couvre une zone bien plus large que le système standard à terre correspondant àplusieurs cellules traditionnelles ce qui peut entraîner des risques de collision des données envoyées par des navireslocalisés dans des cellules différentes et reçues au niveau de l’antenne du satellite. Nous présentons différentes approchesafin de répondre au problème de collision considéré. Elles ne reposent pas toujours sur les mêmes hypothèses en ce quiconcerne les signaux reçus, et ne s’appliquent donc pas toutes dans les mêmes contextes (nombre de capteurs utilisés,mode semi-supervisé avec utilisation de trames d’apprentissage et information a priori ou mode aveugle, problèmes liés àla synchronisation des signaux, etc...).Dans un premier temps, nous proposons des méthodes permettant la séparation/dé-collision des messages en modèle surdéterminé(plus de capteurs que de messages). Elles sont fondées sur des algorithmes de décompositions matriciellesconjointes combinés à des détecteurs de points temps-fréquence (retard-fréquence Doppler) particuliers permettant laconstruction d’ensembles de matrices devant être (bloc) ou zéro (bloc) diagonalisées conjointement. En ce qui concerneles algorithmes de décompositions matricielles conjointes, nous proposons quatre nouveaux algorithmes de blocdiagonalisation conjointe (de même que leur version à pas optimal) fondés respectivement sur des algorithmesd’optimisation de type gradient conjugué, gradient conjugué pré-conditionné, Levenberg-Marquardt et Quasi-Newton. Lecalcul exact du gradient matriciel complexe et des matrices Hessiennes complexes est mené. Nous introduisonségalement un nouveau problème dénommé zéro-bloc diagonalisation conjointe non-unitaire lequel généralise le problèmedésormais classique de la zéro-diagonalisation conjointe non-unitaire. Il implique le choix d’une fonction de coût adaptéeet à nouveau le calcul de quantités telles que gradient matriciel complexe et les matrices Hessiennes complexes. Nousproposons ensuite trois nouveaux algorithmes à pas optimal fondés sur des algorithmes d’optimisation de type gradientconjugué, gradient conjugué pré-conditionné et Levenberg-Marquardt.Finalement, nous terminons par des approches à base de techniques de détection multi-utilisateurs conjointe susceptiblesde fonctionner en contexte sous-déterminé dans lequel nous ne disposons plus que d’un seul capteur recevantsimultanément plusieurs signaux sources. Nous commençons par développer une première approche par déflationconsistant à supprimer successivement les interférences. Nous proposons ensuite un deuxième mode opératoire fondéquant à lui sur l’estimateur du maximum de vraisemblance conjoint qui est une variante de l’algorithme de VITERBI. / This PHD thesis concerns the spatial automatic identification system dedicated to marine surveillance by satellite. Thissystem covers a larger area than the traditional system corresponding to several satellite cells. In such a system, there arerisks of collision of the messages sent by vessels located in different cells and received at the antenna of the samesatellite. We present different approaches to address the considered problem. They are not always based on the sameassumptions regarding the received signals and are not all applied in the same contexts (they depend on the number ofused sensors, semi-supervised mode with use of training sequences and a priori information versus blind mode, problemswith synchronization of signals, etc.). Firstly, we develop several approaches for the source separation/de-collision in theover-determined case (more sensors than messages) using joint matrix decomposition algorithms combined withdetectors of particular time-frequency (delay-Doppler frequency) points to build matrix sets to be joint (block) or zero(block) diagonalized. Concerning joint matrix decomposition algorithms, four new joint block-diagonalization algorithms(with optimal step-size) are introduced based respectively on conjugate gradient, preconditioned conjugate gradient,Levenberg-Marquardt and Quasi-Newton optimization schemes. Secondly, a new problem called non-unitary joint zeroblockdiagonalization is introduced. It encompasses the classical joint zero diagonalization problem. It involves thechoice of a well-chosen cost function and the calculation of quantities such as the complex gradient matrix and thecomplex Hessian matrices. We have therefore proposed three new algorithms (and their optimal step-size version) basedrespectively on conjugate gradient, preconditioned conjugate gradient and Levenberg-Marquardt optimization schemes.Finally, we suggest other approaches based on multi-user joint detection techniques in an underdetermined context wherewe have only one sensor receiving simultaneously several signals. First, we have developed an approach by deflationbased on a successive interferences cancelation technique. Then, we have proposed a second method based on the jointmaximum likelihood sequence estimator which is a variant of the VITERBI algorithm.

La séparation de signaux corrélés à partir de leurs combinaisons linéaires est une tâche difficile et possède plusieurs applications en traitement du signal. Nous étudions deux problèmes, à savoir la séparation aveugle de sources parcimonieuses et le filtrage adaptatif des réflexions multiples en acquisition sismique. Un intérêt particulier est porté sur les mélanges convolutifs : pour ces deux problèmes, des filtres à réponses impulsionnelles finies peuvent être estimés afin de récupérer les signaux désirés.Pour les modèles de mélange instantanés et convolutifs, nous donnons les conditions nécessaires et suffisantes pour l'extraction et la séparation exactes de sources parcimonieuses en utilisant la pseudo-norme L0 comme une fonction de contraste. Des équivalences entre l'analyse en composantes parcimonieuses et l'analyse en composantes disjointes sont examinées.Pour la soustraction adaptative des réflexions sismiques, nous discutons les limites des méthodes basées sur l'analyse en composantes indépendantes et nous soulignons l'équivalence avec les méthodes basées sur les normes Lp. Nous examinons de quelle manière les paramètres de régularisation peuvent être plus décisifs pour l'estimation des primaires. Enfin, nous proposons une amélioration de la robustesse de la soustraction adaptative en estimant les filtres adaptatifs directement dans le domaine des curvelets. Les coûts en calcul et en mémoire peuvent être atténués par l'utilisation de la transformée en curvelet discrète et uniforme. / The recovery of correlated signals from their linear combinations is a challenging task and has many applications in signal processing. We focus on two problems that are the blind separation of sparse sources and the adaptive subtraction of multiple events in seismic processing. A special focus is put on convolutive mixtures: for both problems, finite impulse response filters can indeed be estimated for the recovery of the desired signals.For instantaneous and convolutive mixing models, we address the necessary and sufficient conditions for the exact extraction and separation of sparse sources by using the L0 pseudo-norm as a contrast function. Equivalences between sparse component analysis and disjoint component analysis are investigated.For adaptive multiple subtraction, we discuss the limits of methods based on independent component analysis and we highlight equivalence with Lp-norm-based methods. We investigate how other regularization parameters may have more influence on the estimation of the desired primaries. Finally, we propose to improve the robustness of adaptive subtraction by estimating the extracting convolutive filters directly in the curvelet domain. Computation and memory costs are limited by using the uniform discrete curvelet transform.

Este trabalho estuda o modelo de análise em componentes independentes (ICA) para misturas instantâneas, aplicado na separação de sinais de áudio. Três algoritmos de separação de misturas instantâneas são avaliados: FastICA, PP (Projection Pursuit) e PearsonICA; possuindo dois princípios básicos em comum: as fontes devem ser independentes estatisticamente e não-Gaussianas. Para analisar a capacidade de separação dos algoritmos foram realizados dois grupos de experimentos. No primeiro grupo foram geradas misturas instantâneas, sinteticamente, a partir de sinais de áudio pré-definidos. Além disso, foram geradas misturas instantâneas a partir de sinais com características específicas, também geradas sinteticamente, para avaliar o comportamento dos algoritmos em situações específicas. Para o segundo grupo foram geradas misturas convolutivas no laboratório de acústica do LPS. Foi proposto o algoritmo PP, baseado no método de Busca de Projeções comumente usado em sistemas de exploração e classificação, para separação de múltiplas fontes como alternativa ao modelo ICA. Embora o método PP proposto possa ser utilizado para separação de fontes, ele não pode ser considerado um método ICA e não é garantida a extração das fontes. Finalmente, os experimentos validam os algoritmos estudados. / This work studies Independent Component Analysis (ICA) for instantaneous mixtures, applied to audio signal (source) separation. Three instantaneous mixture separation algorithms are considered: FastICA, PP (Projection Pursuit) and PearsonICA, presenting two common basic principles: sources must be statistically independent and non-Gaussian. In order to analyze each algorithm separation capability, two groups of experiments were carried out. In the first group, instantaneous mixtures were generated synthetically from predefined audio signals. Moreover, instantaneous mixtures were generated from specific signal generated with special features, synthetically, enabling the behavior analysis of the algorithms. In the second group, convolutive mixtures were probed in the acoustics laboratory of LPS at EPUSP. The PP algorithm is proposed, based on the Projection Pursuit technique usually applied in exploratory and clustering environments, for separation of multiple sources as an alternative to conventional ICA. Although the PP algorithm proposed could be applied to separate sources, it couldnt be considered an ICA method, and source extraction is not guaranteed. Finally, experiments validate the studied algorithms.

Um Sistema Elétrico de Potência (SEP) está susceptível à presença de diversas fontes de distúrbios que prejudicam a Qualidade da Energia Elétrica (QEE). Desta forma, as suas tensões e/ou correntes podem conter m´múltiplos distúrbios com ocorrência simultânea. Este trabalho apresenta uma metodologia para decomposição do sinal medido em componentes que estimem as formas de onda dos distúrbios individuais quando da ocorrência de m´múltiplos distúrbios, com o posterior reconhecimento de cada um deles. A Análise de Componentes Independentes (ICA) é utilizada como principal ferramenta na etapa de decomposição dos distúrbios. A ICA é originalmente uma t´técnica aplicada em análise multivariada de dados, o que significa que ela necessita de medições realizadas por múltiplos sensores dispostos em diferentes posições de um sistema. No entanto, este trabalho propõe a sua aplicação tendo disponível apenas um sinal medido. Para tanto, são propostos dois métodos para produzir a diversidade necessária para a t´técnica funcionar adequadamente. É demonstrado que ambos os métodos equivalem a um banco de filtros lineares adaptativos capaz de realizar a separação não-supervisionada de múltiplos distúrbios independentes e que sejam espectralmente disjuntos. Por fim, é proposto um sistema de classificação que utiliza Redes Neurais Artificiais (RNAs) para identificar os distúrbios decompostos pela etapa anterior. A metodologia completa é avaliada por meio de testes utilizando dados sintéticos e reais, alcançando resultados altamente satisfatórios para decomposição de sinais contendo múltiplos distúrbios e taxas de acerto globais dos classificadores superiores a 97% / The power system is susceptible to the presence of several sources of disturbances that harm the power quality. In this sense, its voltages and/or currents may contain multiple disturbances with simultaneous occurrence. This work presents a methodology that decomposes the measured signal in components which estimate the waveforms of the individual disturbances followed by their recognition when a multiple disturbance situation occurs. The Independent Component Analysis (ICA) is the main tool in the disturbance decomposition stage. The ICA is originally a technique applied in multivariate data analysis, which means that it requires measurements from multiple sensors allocated in different positions of the system. However, this work proposes its application for a single measured signal available. For this, two methods were developed in order to provide the required diversity to the ICA technique. It is demonstrated that both methods are equivalent to an adaptive linear filter bank capable to perform an unsupervised separation of multiple independent disturbances, if they are spectrally disjoint. A classification system based on artificial neural networks is proposed to identify the disturbances decomposed by the previous stage. The complete system is tested using synthetic and actual data, presenting highly satisfactory results for the decomposition of signals containing multiple disturbances, and precision for the classification task above 97%

Der Fokus dieser Dissertation liegt auf den Verbindungen zwischen ICA (Independent Component Analysis - Unabhängige Komponenten Analyse) und SFA (Slow Feature Analysis - Langsame Eigenschaften Analyse). Um einen Vergleich zwischen beiden Methoden zu ermöglichen wird CuBICA2, ein ICA Algorithmus basierend nur auf Statistik zweiter Ordnung, d.h. Kreuzkorrelationen, vorgestellt. Dieses Verfahren minimiert zeitverzögerte Korrelationen zwischen Signalkomponenten, um die statistische Abhängigkeit zwischen denselben zu reduzieren. Zusätzlich wird eine alternative SFA-Formulierung vorgestellt, die mit CuBICA2 verglichen werden kann. Im Falle linearer Gemische sind beide Methoden äquivalent falls nur eine einzige Zeitverzögerung berücksichtigt wird. Dieser Vergleich kann allerdings nicht auf mehrere Zeitverzögerungen erweitert werden. Für ICA lässt sich zwar eine einfache Erweiterung herleiten, aber ein ähnliche SFA-Erweiterung kann nicht im originären SFA-Sinne (SFA extrahiert die am langsamsten variierenden Signalkomponenten aus einem gegebenen Eingangssignal) interpretiert werden. Allerdings kann eine im SFA-Sinne sinnvolle Erweiterung hergeleitet werden, welche die enge Verbindung zwischen der Langsamkeit eines Signales (SFA) und der zeitlichen Vorhersehbarkeit desselben verdeutlich. Im Weiteren wird CuBICA2 und SFA kombiniert. Das Resultat kann aus zwei Perspektiven interpretiert werden. Vom ICA-Standpunkt aus führt die Kombination von CuBICA2 und SFA zu einem Algorithmus, der das Problem der nichtlinearen blinden Signalquellentrennung löst. Vom SFA-Standpunkt aus ist die Kombination eine Erweiterung der standard SFA. Die standard SFA extrahiert langsam variierende Signalkomponenten die untereinander unkorreliert sind, dass heißt statistisch unabhängig bis zur zweiten Ordnung. Die Integration von ICA führt nun zu Signalkomponenten die mehr oder weniger statistisch unabhängig sind. / Within this thesis, we focus on the relation between independent component analysis (ICA) and slow feature analysis (SFA). To allow a comparison between both methods we introduce CuBICA2, an ICA algorithm based on second-order statistics only, i.e.\ cross-correlations. In contrast to algorithms based on higher-order statistics not only instantaneous cross-correlations but also time-delayed cross correlations are considered for minimization. CuBICA2 requires signal components with auto-correlation like in SFA, and has the ability to separate source signal components that have a Gaussian distribution. Furthermore, we derive an alternative formulation of the SFA objective function and compare it with that of CuBICA2. In the case of a linear mixture the two methods are equivalent if a single time delay is taken into account. The comparison can not be extended to the case of several time delays. For ICA a straightforward extension can be derived, but a similar extension to SFA yields an objective function that can not be interpreted in the sense of SFA. However, a useful extension in the sense of SFA to more than one time delay can be derived. This extended SFA reveals the close connection between the slowness objective of SFA and temporal predictability. Furthermore, we combine CuBICA2 and SFA. The result can be interpreted from two perspectives. From the ICA point of view the combination leads to an algorithm that solves the nonlinear blind source separation problem. From the SFA point of view the combination of ICA and SFA is an extension to SFA in terms of statistical independence. Standard SFA extracts slowly varying signal components that are uncorrelated meaning they are statistically independent up to second-order. The integration of ICA leads to signal components that are more or less statistically independent.

L'étude par neuro-imagerie de l'activité de plusieurs cerveaux en interaction (hyperscanning) permet d'étendre notre compréhension des neurosciences sociales. Nous proposons un cadre pour l'hyperscanning utilisant les interfaces cerveau-ordinateur multi-utilisateur qui inclut différents paradigmes sociaux tels que la coopération ou la compétition. Les travaux de cette thèse comportent trois contributions interdépendantes. Notre première contribution est le développement d'une plateforme expérimentale sous la forme d'un jeu vidéo multijoueur, nommé Brain Invaders 2, contrôlé par la classification de potentiels évoqués visuels enregistrés par électroencéphalographie (EEG). Cette plateforme est validée par deux protocoles expérimentaux comprenant dix-neuf et vingt-deux paires de sujets et utilise différentes approches de classification adaptative par géométrie riemannienne. Ces approches sont théoriquement et expérimentalement comparées et nous montrons la supériorité de la fusion des classifieurs indépendants sur la classification d'un hypercerveau durant la seconde contribution. L'analyse de coïncidence des signaux entre les individus est une approche classique pour l'hyperscanning, elle est pourtant difficile quand les signaux EEG concernés sont transitoires avec une grande variabilité (intra- et inter-sujet) spatio-temporelle et avec un faible rapport signal-à-bruit. En troisième contribution, nous proposons un nouveau modèle composite de séparation aveugle de sources physiologiquement plausibles permettant de compenser cette variabilité. Une solution par diagonalisation conjointe approchée est proposée avec une implémentation d'un algorithme de type Jacobi. A partir des données de Brain Invaders 2, nous montrons que cette solution permet d'extraire simultanément des sources d'artéfacts, des sources d'EEG évoquées et des sources d'EEG continues avec plus de robustesse et de précision que les modèles existants. / The study of several brains interacting (hyperscanning) with neuroimagery allows to extend our understanding of social neurosciences. We propose a framework for hyperscanning using multi-user Brain-Computer Interfaces (BCI) that includes several social paradigms such as cooperation or competition. This dissertation includes three interdependent contribution. The first contribution is the development of an experimental platform consisting of a multi-player video game, namely Brain Invaders 2, controlled by classification of visual event related potentials (ERP) recorded by electroencephalography (EEG). The plateform is validated through two experimental protocols including nineteen and twenty two pairs of subjects while using different adaptive classification approaches using Riemannian geometry. Those approaches are theoretically and experimentally compared during the second contribution ; we demonstrates the superiority in term of accuracy of merging independent classifications over the classification of the hyperbrain during the second contribution. Analysis of inter-brain synchronizations is a common approach for hyperscanning, however it is challenging for transient EEG waves with an great spatio-temporal variability (intra- and inter-subject) and with low signal-to-noise ratio such as ERP. Therefore, as third contribution, we propose a new blind source separation model, namely composite model, to extract simultaneously evoked EEG sources and ongoing EEG sources that allows to compensate this variability. A solution using approximate joint diagonalization is given and implemented with a fast Jacobi-like algorithm. We demonstrate on Brain Invaders 2 data that our solution extracts simultaneously evoked and ongoing EEG sources and performs better in term of accuracy and robustness compared to the existing models.

Um Sistema Elétrico de Potência (SEP) está susceptível à presença de diversas fontes de distúrbios que prejudicam a Qualidade da Energia Elétrica (QEE). Desta forma, as suas tensões e/ou correntes podem conter m´múltiplos distúrbios com ocorrência simultânea. Este trabalho apresenta uma metodologia para decomposição do sinal medido em componentes que estimem as formas de onda dos distúrbios individuais quando da ocorrência de m´múltiplos distúrbios, com o posterior reconhecimento de cada um deles. A Análise de Componentes Independentes (ICA) é utilizada como principal ferramenta na etapa de decomposição dos distúrbios. A ICA é originalmente uma t´técnica aplicada em análise multivariada de dados, o que significa que ela necessita de medições realizadas por múltiplos sensores dispostos em diferentes posições de um sistema. No entanto, este trabalho propõe a sua aplicação tendo disponível apenas um sinal medido. Para tanto, são propostos dois métodos para produzir a diversidade necessária para a t´técnica funcionar adequadamente. É demonstrado que ambos os métodos equivalem a um banco de filtros lineares adaptativos capaz de realizar a separação não-supervisionada de múltiplos distúrbios independentes e que sejam espectralmente disjuntos. Por fim, é proposto um sistema de classificação que utiliza Redes Neurais Artificiais (RNAs) para identificar os distúrbios decompostos pela etapa anterior. A metodologia completa é avaliada por meio de testes utilizando dados sintéticos e reais, alcançando resultados altamente satisfatórios para decomposição de sinais contendo múltiplos distúrbios e taxas de acerto globais dos classificadores superiores a 97% / The power system is susceptible to the presence of several sources of disturbances that harm the power quality. In this sense, its voltages and/or currents may contain multiple disturbances with simultaneous occurrence. This work presents a methodology that decomposes the measured signal in components which estimate the waveforms of the individual disturbances followed by their recognition when a multiple disturbance situation occurs. The Independent Component Analysis (ICA) is the main tool in the disturbance decomposition stage. The ICA is originally a technique applied in multivariate data analysis, which means that it requires measurements from multiple sensors allocated in different positions of the system. However, this work proposes its application for a single measured signal available. For this, two methods were developed in order to provide the required diversity to the ICA technique. It is demonstrated that both methods are equivalent to an adaptive linear filter bank capable to perform an unsupervised separation of multiple independent disturbances, if they are spectrally disjoint. A classification system based on artificial neural networks is proposed to identify the disturbances decomposed by the previous stage. The complete system is tested using synthetic and actual data, presenting highly satisfactory results for the decomposition of signals containing multiple disturbances, and precision for the classification task above 97%

Ces travaux de thèse concernent le développement de nouvelles méthodes de séparation aveugle de mélanges linéaires instantanés pour des applications à des données hyperspectrales en astrophysique. Nous avons proposé trois approches pour effectuer la séparation des données. Une première contribution est fondée sur l'hybridation de deux méthodes existantes de séparation aveugle de source (SAS) : la méthode SpaceCORR nécessitant une hypothèse de parcimonie et une méthode de factorisation en matrices non négatives (NMF). Nous montrons que l'utilisation des résultats de SpaceCORR pour initialiser la NMF permet d'améliorer les performances des méthodes utilisées seules. Nous avons ensuite proposé une première méthode originale permettant de relâcher la contrainte de parcimonie de SpaceCORR. La méthode MASS (pour \textit{Maximum Angle Source Separation}) est une méthode géométrique basée sur l'extraction de pixels mono-sources pour réaliser la séparation des données. Nous avons également étudié l'hybridation de MASS avec la NMF. Enfin, nous avons proposé une seconde approche permettant de relâcher la contrainte de parcimonie de SpaceCORR. La méthode originale SIBIS (pour \textit{Subspace-Intersection Blind Identification and Separation}) est une méthode géométrique basée sur l'identification de l'intersection de sous-espaces engendrés par des régions de l'image hyperspectrale. Ces intersections permettent, sous une hypothèse faible de parcimonie, de réaliser la séparation des données. L'ensemble des approches proposées dans ces travaux ont été validées par des tests sur données simulées puis appliquées sur données réelles. Les résultats obtenus sur ces données sont très encourageants et sont comparés à ceux obtenus par des méthodes de la littérature. / This thesis deals with the development of new blind separation methods for linear instantaneous mixtures applicable to astrophysical hyperspectral data sets. We propose three approaches to perform data separation. A first contribution is based on hybridization of two existing blind source separation (BSS) methods: the SpaceCORR method, requiring a sparsity assumption, and a non-negative matrix factorization (NMF) method. We show that using SpaceCORR results to initialize the NMF improves the performance of the methods used alone. We then proposed a first original method to relax the sparsity constraint of SpaceCORR. The method called MASS (Maximum Angle Source Separation) is a geometric method based on the extraction of single-source pixels to achieve the separation of data. We also studied the hybridization of MASS with the NMF. Finally, we proposed an approach to relax the sparsity constraint of SpaceCORR. The original method called SIBIS (Subspace-Intersection Blind Identification and Separation) is a geometric method based on the identification of intersections of subspaces generated by regions of the hyperspectral image. Under a sparsity assumption, these intersections allow one to achieve the separation of the data. The approaches proposed in this manuscript have been validated by experimentations on simulated data and then applied to real data. The results obtained on our data are very encouraging and are compared with those obtained by methods from the literature.

Cette thèse développe des méthodes de diagonalisation conjointe de matrices et de tenseurs d’ordre trois, et son application à la séparation MIMO de sources de télécommunications numériques. Après un état, les motivations et objectifs de la thèse sont présentés. Les problèmes de la diagonalisation conjointe et de la séparation de sources sont définis et un lien entre ces deux domaines est établi. Par la suite, plusieurs algorithmes itératifs de type Jacobi reposant sur une paramétrisation LU sont développés. Pour chacun des algorithmes, on propose de déterminer les matrices permettant de diagonaliser l’ensemble considéré par l’optimisation d’un critère inverse. On envisage la minimisation du critère selon deux approches : la première, de manière directe, et la seconde, en supposant que les éléments de l’ensemble considéré sont quasiment diagonaux. En ce qui concerne l’estimation des différents paramètres du problème, deux stratégies sont mises en œuvre : l’une consistant à estimer tous les paramètres indépendamment et l’autre reposant sur l’estimation indépendante de couples de paramètres spécifiquement choisis. Ainsi, nous proposons trois algorithmes pour la diagonalisation conjointe de matrices complexes symétriques ou hermitiennes et deux algorithmes pour la diagonalisation conjointe d’ensembles de tenseurs symétriques ou non-symétriques ou admettant une décomposition INDSCAL. Nous montrons aussi le lien existant entre la diagonalisation conjointe de tenseurs d’ordre trois et la décomposition canonique polyadique d’un tenseur d’ordre quatre, puis nous comparons les algorithmes développés à différentes méthodes de la littérature. Le bon comportement des algorithmes proposés est illustré au moyen de simulations numériques. Puis, ils sont validés dans le cadre de la séparation de sources de télécommunications numériques. / This thesis develops joint diagonalization of matrices and third-order tensors methods for MIMO source separation in the field of digital telecommunications. After a state of the art, the motivations and the objectives are presented. Then the joint diagonalisation and the blind source separation issues are defined and a link between both fields is established. Thereafter, five Jacobi-like iterative algorithms based on an LU parameterization are developed. For each of them, we propose to derive the diagonalization matrix by optimizing an inverse criterion. Two ways are investigated : minimizing the criterion in a direct way or assuming that the elements from the considered set are almost diagonal. Regarding the parameters derivation, two strategies are implemented : one consists in estimating each parameter independently, the other consists in the independent derivation of couple of well-chosen parameters. Hence, we propose three algorithms for the joint diagonalization of symmetric complex matrices or hermitian ones. The first one relies on searching for the roots of the criterion derivative, the second one relies on a minor eigenvector research and the last one relies on a gradient descent method enhanced by computation of the optimal adaptation step. In the framework of joint diagonalization of symmetric, INDSCAL or non symmetric third-order tensors, we have developed two algorithms. For each of them, the parameters derivation is done by computing the roots of the considered criterion derivative. We also show the link between the joint diagonalization of a third-order tensor set and the canonical polyadic decomposition of a fourth-order tensor. We confront both methods through numerical simulations. The good behavior of the proposed algorithms is illustrated by means of computing simulations. Finally, they are applied to the source separation of digital telecommunication signals.

Many of the existing ambient modal identification methods based on vibration data process information centrally to calculate the modal properties. Such methods demand relatively large memory and processing capabilities to interrogate the data. With the recent advances in wireless sensor technology, it is now possible to process information on the sensor itself. The decentralized information so obtained from individual sensors can be combined to estimate the global modal information of the structure. The main objective of this thesis is to present a new class of decentralized algorithms that can address the limitations stated above. The completed work in this regard involves casting the identification problem within the framework of underdetermined blind source separation (BSS). Time-frequency transformations of measurements are carried out, resulting in a sparse representation of the signals. Stationary wavelet packet transform (SWPT) is used as the primary means to obtain a sparse representation in the time-frequency domain. Several partial setups are used to obtain the partial modal information, which are then combined to obtain the global structural mode information. Most BSS methods in the context of modal identification assume that the excitation is white and do not contain narrow band excitation frequencies. However, this assumption is not satisfied in many situations (e.g., pedestrian bridges) when the excitation is a superposition of narrow-band harmonic(s) and broad-band disturbance. Under such conditions, traditional BSS methods yield sources (modes) without any indication as to whether the identified source(s) is a system or an excitation harmonic. In this research, a novel under-determined BSS algorithm is developed involving statistical characterization of the sources which are used to delineate the sources corresponding to external disturbances versus intrinsic modes of the system. Moreover, the issue of computational burden involving an over-complete dictionary of sparse bases is alleviated through a new underdetermined BSS method based on a tensor algebra tool called PARAllel FACtor (PARAFAC) decomposition. At the core of this method, the wavelet packet decomposition coefficients are used to form a covariance tensor, followed by PARAFAC tensor decomposition to separate the modal responses. Finally, the proposed methods are validated using measurements obtained from both wired and wireless sensors on laboratory scale and full scale buildings and bridges.