Independent component analysis on spectral domain

Independent component analysis (ICA) is an effective data-driven method for blind source separation. It has been successfully applied to separate source signals of interest from their mixtures. Most existing ICA procedures are carried out by relying solely on the estimation of the marginal density functions, either parametrically or nonparametrically. In many applications, correlation structures within each source also play an important role besides the marginal distributions. One important example is functional magnetic resonance imaging (fMRI) analysis where the brain-function-related signals are temporally correlated. In this thesis, we propose two novel ICA algorithms that fully exploit the correlation structures within the source signals through spectral density estimation. Our methodology development is two-fold: 1) ICA for auto-correlated sources via parametric spectral density estimation (cICA-YW); 2) ICA for sources with mixed spectra via nonparametric spectral density estimation and atom detection (cICA-LSP). The cICA-YW focuses on the sources with autocorrelation and is implemented using spectral density functions from frequently used time series models such as autoregressive moving average (ARMA) processes. The time series parameters and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies and a real fMRI application. The numerical results indicate that our approach outperforms several popular methods including the most widely used fastICA algorithm. We also establish the sampling properties of the proposed method. For the cICA-LSP, we consider the case of sources with possibly mixed spectra, where ARMA estimates are often unstable. Specifically, we propose to estimate the spectral density functions and the line spectra of the source signals using cubic splines and indicator functions, respectively. The mixed spectra and the mixing matrix are estimated via maximizing the Whittle likelihood function. We illustrate the performance of the proposed method through extensive simulation studies.Doctor of Philosoph

Modélisation cyclostationnaire et séparation de sources des signaux électromyographiques

The aim of this thesis is to develop decomposition methods of electromyographic (EMG) signals into elementary signals, called motor unit action potential trains (MUAPT). We proposed two signal generation models and we have demonstrated the cyclostationary and fuzzy cyclostationary properties of these. We finally proposed a blind decomposition method from multi-sensor EMG signals using these properties. We present the theoretical limitations of the method, in particular the existence of a limiting threshold of the discharge frequency. We conducted a performance evaluation of the proposed method with a comparison with conventional 2nd order separation method. It has been shown that the contribution of cyclostationarity property brings better performance in noisy and noiseless cases and in the cyclostationary and fuzzy cyclostationary model cases. We highlighted a performance degradation when the discharge frequency was beyond the theoretical threshold. This evaluation was performed via Monte Carlo simulations based on real observations. Finally, we presented real EMG signals results. The method has shown good results on intramuscular EMG signals.L’objectif de cette thèse est de développer des méthodes de décomposition des signaux électromyographiques (EMG) en signaux élémentaires, les trains de potentiels d’action d’unité motrice (TPAUM). Nous avons proposé deux modèles de génération des signaux et nous avons mis en évidence la propriété de cyclostationnarité et de cyclostationnarité floue de ces deux modèles. Dans l’objectif de la décomposition, nous avons enfin proposé une méthode de décomposition aveugle à partir de signaux EMG multi-capteurs en utilisant cette propriété. Nous présentons les limitations théoriques de la méthode, notamment par un seuil limite de la fréquence de décharge. Nous avons effectué une évaluation des performances de la méthode proposée avec comparaison à une méthode classique de séparation à l’ordre 2.Il a été montré que l’exploitation de la propriété de cyclostationnarité apportait de meilleures performances de séparation dans le cas bruité et non bruité, sur le modèle cyclostationnaire et sur le modèle cyclostationnaire flou. Les performances se trouvent dégradées lorsque la fréquence de décharge dépasse le seuil théorique. Cette évaluation a été réalisée au moyen de simulations de Monte-Carlo construites sur des observations réelles. Enfin, la méthode appliquée sur des données réelles a montré de bons résultats sur des signaux EMG intramusculaires