Une généralisation de l'algorithme JADE

On considère le problème de la séparation de sources basée sur la diagonalisation conjointe d'un ensemble de matrices. L'algorithme JADE atteint cet objectif en utilisant des matrices de cumulants d'ordre quatre. Nous nous proposons dans cette communication de généraliser le contraste sur lequel repose JADE et son lien avec un critère de diagonalisation conjointe en l'étendant à des cumulants d'ordre quelconque supérieur ou égal à trois. L'intérêt principal est alors de pouvoir choisir l'ordre des cumulants ou de combiner des matrices de cumulants d'ordres différents

Fonctions de contraste et cumulants croisés pour la séparation de mélanges convolutifs

Nous considérons le problème de la séparation de mélanges de signaux statistiquement indépendants en contexte convolutif. Notre approche est fondée sur la maximisation de fonctions de contraste. Après un rappel préalable de la définition des fonctions de contraste, nous montrons que dans le cadre des mélanges convolutifs, on peut considérer des contrastes comportant des cumulants croisés. Quatre nouveaux contrastes contenant des cumulants croisés sont donc introduits, l'un d'eux généralise au cas convolutif celui de [1], deux des quatre autres sont intermédiaires entre le contraste de P. Comon [3] et le précédent. Enfin le dernier se révèle spécifique au cas des mélanges convolutifs

Advanced robust non-invasive foetal heart detection techniques during active labour using one pair of transabdominal electrodes

The thesis proposes and evaluates three state-of-the-art signal processing techniques to detect fetal heartbeats within each maternal cardiac cycle, during labour contractions, using only a pair of transabdominal electrodes. The first and second techniques are, namely, the structured third- order cumulant-slice-template matching and the bispectral-contours-template matching for fetal QRS identification, respectively. The third technique is based on the modified and appropriately weighted spectral multiple signal classification (MUSIC) with incorporated covariance matrix for uterine contraction noise-like interfering signals also contaminated with noise. Essentially, two modifications to the standard MUSIC have been developed in order to enhance the performance of the spectral estimator in our applied work. The first modification involves the introduction of an optimised weighting function to the segmented ECG covariance matrix, and is chiefly aimed at enhancing the fetal QRS major spectral peak which occurs at around 30 Hz against the mother QRS major spectral peak usually occurring around 17 Hz and all other noise contributions. Additional optional pseudo-bispectral enhancement to sharpen the maternal and fetal spectral peaks, in particular when the mother and fetal R-waves are temporally coincident, have been achieved. The second modification to the spectral MUSIC is the removal of the unjustified assumption that only white Gaussian noise is present and the incorporation of the actual measured labour uterine contraction covariance matrix in reconfigured subspace analysis. This inevitably leads to the generalised eigenvectors - eigenvalues decomposition modern signal processing. This is now coined the modified, interference incorporated pseudo-spectral MUSIC. The above mentioned first and second techniques are higher-order statistics-based (HOS) and hybrid involving both signal processing and NN classifiers. The third technique is second-order statistics-based (SOS). In all techniques, the removal of signal non-linearity with the aid of non-linear Volterra synthesisers plays a crucial part in the fetal detection integrity. Accurately assessed fetal heart classification rates as high as 95% have been achieved during labour, thus helping to provide non-invasive transparency to fetal intrapartum welfare. Performance analysis and evaluation processes involved more than 30 critical cases classified as “fetal under stress in labour” recorded in a London hospital database and used both transbadominal ECG electrodes and fetal scalp electrodes. The latter facilitates detection of the instantaneous fetal heart rate which is then used as the Reference Fetal Heart Rate in the assessment of the classification rate of each of the above mentioned techniques. It will be shown that the fetal heartbeats are completely masked by uterine activity and noise artefacts in all the recorded transabdominal maternal ECG signals. The fetal scalp electrode was, therefore, deemed necessary to provide the highest accurate measure of fetal heart functionality (from the hospital viewpoint), and in the assessment of the three non-invasive techniques presented in this thesis. The techniques may also be used during gestation and as early as 10 weeks