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<p>The need for fast multidimensional signal processing arises in many areas. One of the more demanding applications is real time visualization of medical data acquired with e.g. magnetic resonance imaging where large amounts of data can be generated. This data has to be reduced to relevant clinical information, either by image reconstruction and enhancement or automatic feature extraction. Design of fast-acting multidimensional filters has been subject to research during the last three decades. Usually methods for fast filtering are based on applying a sequence of filters of lower dimensionality acquired by e.g. weighted low-rank approximation. Filter networks is a method to design fast multidimensional filters by decomposing multiple filters into simpler filter components in which coefficients are allowed to be sparsely scattered. Up until now, coefficient placement has been done by hand, a procedure which is time-consuming and difficult. The aim of this thesis is to investigate whether genetic algorithms can be used to place coefficients in filter networks. A method is developed and tested on 2-D filters and the resulting filters have lower distortion values while still maintaining the same or lower number of coefficients than filters designed with previously known methods.</p>

The need for fast multidimensional signal processing arises in many areas. One of the more demanding applications is real time visualization of medical data acquired with e.g. magnetic resonance imaging where large amounts of data can be generated. This data has to be reduced to relevant clinical information, either by image reconstruction and enhancement or automatic feature extraction. Design of fast-acting multidimensional filters has been subject to research during the last three decades. Usually methods for fast filtering are based on applying a sequence of filters of lower dimensionality acquired by e.g. weighted low-rank approximation. Filter networks is a method to design fast multidimensional filters by decomposing multiple filters into simpler filter components in which coefficients are allowed to be sparsely scattered. Up until now, coefficient placement has been done by hand, a procedure which is time-consuming and difficult. The aim of this thesis is to investigate whether genetic algorithms can be used to place coefficients in filter networks. A method is developed and tested on 2-D filters and the resulting filters have lower distortion values while still maintaining the same or lower number of coefficients than filters designed with previously known methods.

Quincunx filter banks are two-dimensional, two-channel, nonseparable filter banks. They are widely used in many signal processing applications. In this thesis, we study the design and applications of quincunx filter banks in the processing of two-dimensional digital signals. Symmetric extension algorithms for quincunx filter banks are proposed. In the one-dimensional case,symmetric extension is a commonly used technique to build nonexpansive transforms of finite-length sequences. We show how this technique can be extended to the nonseparable quincunx case. We consider three types of quadrantally-symmetric linear-phase quincunx filter banks, and for each of these types we show how nonexpansive transforms of two-dimensional sequences defined on arbitrary rectangular regions can be constructed. New optimization-based techniques are proposed for the design of high-performance quincunx filter banks for the application of image coding. The new methods yield linear-phase perfect-reconstruction systems with high coding gain, good analysis/synthesis filter frequency responses, and certain prescribed vanishing moment properties. We present examples of filter banks designed with these techniques and demonstrate their efficiency for image coding relative to existing filter banks. The best filter banks in our design examples outperformother previously proposed quincunx filter banks in approximately 80% cases and sometimes even outperform the well-known 9/7 filter bank from the JPEG-2000 standard.

Cette thèse est consacrée à l'étude de la localisation d'objets enfouis dans acoustiques sous-marins en utilisant les méthodes de traitement d'antenne et les ondes acoustiques. Nous avons proposé un modèle bien adapté en tenant compte le phénomène physique au niveau de l'interface eau/sédiment. La modélisation de la propagation combine donc la contribution de l'onde réfléchie et celle de l'onde réfractée pour déterminer un nouveau vecteur directionnel. Le vecteur directionnel élaboré à partir des modèles de diffusion acoustique est utilisé dans la méthode MUSIC au lieu d'utiliser le modèle d'onde plane habituel. Cette approche permet d'estimer à la fois coordonnées d'objets (angle et distance objet-capteur) de forme connue, quel que soit leur emplacement vis à vis de l'antenne, en champ proche ou en champ lointain. Nous remplaçons l'étape de décomposition en éléments propres par des algorithmes plus rapides. Nous développons un algorithme d'optimisation plus élaboré consiste à combiner l'algorithme DIRECT (DIviding RECTangles) avec une interpolation de type Spline, ceci permet de faire face au cas d'antennes distordues à grand nombre de capteurs, tout en conservant un temps de calcul faible. Les signaux reçus sont des signaux issus de ce même capteur, réfléchis et réfractés par les objets et sont donc forcément corrélés. Pour cela, nous d'abord utilisons un opérateur bilinéaire. Puis nous proposons une méthode pour le cas de groupes indépendants de signaux corrélés en utilisant les cumulants. Ensuit nous présentons une méthode en utilisant la matrice tranche cumulants pour éliminer du bruit Gaussien. Mais dans la pratique, le bruit n'est pas toujours gaussien ou ses caractéristiques ne sont pas toujours connues. Nous développons deux méthodes itératives pour estimer la matrice interspectrale du bruit. Le premier algorithme est basé sur une technique d'optimisation permettant d'extraire itérativement la matrice interspectrale du bruit de la matrice interspectrale des observations. Le deuxième algorithme utilise la technique du maximum de vraisemblance pour estimer conjointement les paramètres du signal et du bruit. Enfin nous testons les algorithmes proposés avec des données expérimentales et les performances des résultats sont très bonnes. / This thesis is devoted to the study of the localization of objects buried in underwater acoustic using array processing methods and acoustic waves. We have proposed a appropriate model, taking into account the water/sediment interface. The propagation modeling thus combines the reflected wave and the refracted wave to determine a new directional vector. The directional vector developed by acoustic scattering model is used in the MUSIC method instead of the classical plane wave model. This approach can estimate both of the object coordinates (angle and distance sensor-object) of known form, in near field or far field. We propose some fast algorithms without eigendecompostion. We combine DIRECT algorithm with spline interpolation to cope with the distorted antennas of many sensors, while maintaining a low computation time. To decorrelate the received signals, we firstly use a bilinear operator. We propose a method for the case of independent groups of correlated signals using the cumulants. Then we present a method using the cumulants matrix to eliminate Gaussian noise. But in practice, the noise is not always Gaussian or the characteristics are not always known. We develope two iterative methods to estimate the interspectral matrix of noise. The first algorithm is based on an optimization technique to extract iteratively the interspectral matrix of noise. The second algorithm uses the technique of maximum likelihood to estimate the signal parameters and the noise. Finally we test the proposed algorithms with experimental data. The results quality is very good.