In order to achieve more realistic visual effect, the texturing mapping has become a very important and popular technique used in three-dimensional (3D) graphic. Many advanced rendering effects including shadow, environment, and bump mapping all depend on various applications of texturing function. Therefore, how to design an efficient texture unit is very important for 3D graphic rendering system. This thesis proposes an advanced texture unit design targeted for the rendering system with the fill rate of two fragments per cycle. This unit can support various filtering functions including nearest neighbor, bi-linear and tri-linear filtering. It can also provide the mip-map function to automatically select the best texture images for rendering. In order to realize the high texel throughput requirement for some complex filtering function, the texture cache has been divided into four banks such that up to eight texels can be delivered every cycle. The data-path design for the filtering unit has adopted the common expression sharing technique to reduce the required arithmetic units. The proposed texturing unit architecture has been implemented and embedded into a 3D rendering accelerator which has been integrated with OpenGL-ES software module, Linux operation system and geometry module, and successfully prototyped on the ARM versatile platform. With the 0.18um technology, this unit can run up to 150 Mhz, and provide the peak throughput of 1.2G texel/s.

Cette thèse traite - en trois essais - de problèmes de choix de portefeuille en situation d’information partielle, thématique que nous présentons dans une courte introduction. Les essais développés abordent chacun une particularité de cette problématique. Le premier (coécrit avec M. Jeanblanc et V. Lacoste) traite la question du choix de la stratégie optimale pour un problème de maximisation d’utilité terminale lorsque l’évolution des prix est modélisée par un processus de Itô-Lévy dont la tendance et l’intensité des sauts ne sont pas observées. L’approche consiste à réécrire le problème initial comme un problème réduit dans la filtration engendrée par les prix. Cela nécessite la dérivation des équations de filtrage non-linéaire, que nous développons pour un processus de Lévy. Le problème est ensuite résolu en utilisant la programmation dynamique par les équations de Bellman et de HJB. Le second essai aborde dans un cadre gaussien la question du coût de l’incertitude, que nous définissons comme la différence entre les stratégies optimales (ou les richesses maximales) d’un agent parfaitement informé et d’un agent partiellement informé. Les propriétés de ce coût de l’information sont étudiées dans le cadre des trois formes standard de fonctions d’utilités et des exemples numériques sont présentés. Enfin, le troisième essai traite la question du choix de portefeuille quand l’information sur les prix de marché n’est disponible qu’à des dates discrètes et aléatoires. Cela revient à supposer que la dynamique des prix suit un processus marqué. Dans ce cadre, nous développons les équations de filtrage et réécrivons le problème initial dans sa forme réduite dans la filtration discrète des prix. Les stratégies optimales sont ensuite calculées en utilisant le calcul de Malliavin pour des mesures aléatoires et une extension de la formule de Clark-Ocone-Haussman est à cette fin présentée. / This thesis deals - in three essays - with problems of choice of portfolio in situation of partial information, thematic that we present in a short introduction. The tests developed each address a particularity of this problem. The first (co-written with M. Jeanblanc and V. Lacoste) deals with the choice of the optimal strategy for a terminal utility maximization problem when the evolution of prices is modeled by an Itô- Lévy process whose trend and the intensity of the jumps are not observed. The approach is to rewrite the initial problem as a reduced problem in price-driven fi ltration. This requires the derivation of nonlinear filtering equations, which we develop for a Lévy process. The problem is then solved using dynamic programming by the Bellman and HJB equations. The second essay tackles the question of the cost of uncertainty in a Gaussian framework, which we de fi ne as the di ff erence between the optimal strategies (or the maximum wealth) of a fully informed agent and a partially informed agent. The properties of this information cost are studied in the context of the three standard forms of utility functions and numericalexamples are presented. Finally, the third essay addresses the issue of portfolio choice when market price information is only available on discrete and random dates. This amounts to assuming that price dynamics follow a marked process. In this framework, we develop fi ltering equations and rewrite the initialproblem in its reduced form in discrete price fi ltration. The optimal strategies are then calculated using Malliavin's computation for random measurements and an extension of the Clark-Ocone-Haussman formula is for this purpose presented.

This masters thesis is focused on filtering the ECG signal for suppression of spurious frequency components of the network. The theoretical part is talking about electrocardiography, ECG signal interference and about principle different types of filtration. In practical part of this thesis are described linear filtering methods and wavelet transform methods with discrete time. The main topic of this work is recommended the best type of filtration.

In this paper we present examples of ground roll attenuation for synthetic and real data gathers by using Contourlet and Curvelet transforms. These non-separable wavelet transforms are locoalized both (x,t)- and (k,f)-domains and allow for adaptive seperation of signal and ground roll. Both linear and non-linear filtering are discussed using the unique properties of these basis that allow for simultaneous localization in the both domains. Eventhough, the linear filtering techniques are encouraging the true added value of these basis-function techniques becomes apparent when we use these decompositions to adaptively substract modeled ground roll from data using a non-linear thesholding procedure. We show real and synthetic examples and the results suggest that these directional-selective basis functions provide a usefull tool for the removal of coherent noise such as ground roll

Cette thèse s'intéresse au problème du positionnement (position et orientation) dans un contexte de réalité augmentée et aborde spécifiquement les solutions à base de capteurs embarqués. Aujourd'hui, les systèmes de navigation vision-inertiel commencent à combler les besoins spécifiques de cette application. Néanmoins, ces systèmes se basent tous sur des corrections de trajectoire issues des informations visuelles à haute fréquence afin de pallier la rapide dérive des capteurs inertiels bas-coûts. Pour cette raison, ces méthodes sont mises en défaut lorsque l'environnement visuel est défavorable.Parallèlement, des travaux récents menés par la société Sysnav ont démontré qu'il était possible de réduire la dérive de l'intégration inertielle en exploitant le champ magnétique, grâce à un nouveau type d'UMI bas-coût composée – en plus des accéléromètres et gyromètres traditionnels – d'un réseau de magnétomètres. Néanmoins, cette méthode est également mise en défaut si des hypothèses de non-uniformité et de stationnarité du champ magnétique ne sont pas vérifiées localement autour du capteur.Nos travaux portent sur le développement d'une solution de navigation à l'estime robuste combinant toutes ces sources d'information: magnétiques, visuelles et inertielles.Nous présentons plusieurs approches pour la fusion de ces données, basées sur des méthodes de filtrage ou d’optimisation et nous développons un modèle de prédiction du champ magnétique inspiré d'approximation proposées en inertiel et permettant d’intégrer efficacement des termes magnétiques dans les méthodes d’ajustement de faisceaux. Les performances de ces différentes approches sont évaluées sur des données réelles et nous démontrons le bénéfice de la fusion de données comparées aux solutions vision-inertielles ou magnéto-inertielles. Des propriétés théoriques de ces méthodes liées à la théorie de l’invariance des estimateurs sont également étudiées. / This thesis addresses the issue of positioning in 6-DOF that arises from augmented reality applications and focuses on embedded sensors based solutions.Nowadays, the performance reached by visual-inertial navigation systems is starting to be adequate for AR applications. Nonetheless, those systems are based on position correction from visual sensors involved at a relatively high frequency to mitigate the quick drift of low-cost inertial sensors. This is a problem when the visual environment is unfavorable.In parallel, recent works have shown it was feasible to leverage magnetic field to reduce inertial integration drift thanks to a new type of low-cost sensor, which includes – in addition to the accelerometers and gyrometers – a network of magnetometers. Yet, this magnetic approach for dead-reckoning fails if stationarity and non-uniformity hypothesis on the magnetic field are unfulfilled in the vicinity of the sensor.We develop a robust dead-reckoning solution combining simultaneously information from all these sources: magnetic, visual, and inertial sensor. We present several approaches to solve for the fusion problem, using either filtering or non-linear optimization paradigm and we develop an efficient way to use magnetic error term in a classical bundle adjustment that was inspired from already used idea for inertial terms. We evaluate the performance of these estimators on data from real sensors. We demonstrate the benefits of the fusion compared to visual-inertial and magneto-inertial solutions. Finally, we study theoretical properties of the estimators that are linked to invariance theory.

Non-linear Bayesian estimation, or estimation of the state of a non-linear stochastic system from a set of indirect noisy measurements is a problem encountered in several fields of science. The particle filter and the ensemble Kalman filter are both used to get sub-optimal solutions of Bayesian inference problems, particularly for high-dimensional non-Gaussian and non-linear models. Both are essentially Monte Carlo techniques that compute their results using a set of estimated trajectories of the variable to be monitored. It has been shown that in a linear and Gaussian environment, solutions obtained from both these filters converge to the optimal solution obtained by the Kalman Filter. However, it is of interest to explore how the two filters compare to each other in basic methodology and construction, especially due to the similarity between them. In this work, we take up a specific problem of Bayesian inference in a restricted framework and compare analytically the results obtained from the particle filter and the ensemble Kalman filter. We show that for the chosen model, under certain assumptions, the two filters become methodologically analogous as the sample size goes to infinity.

Non-linear Bayesian estimation, or estimation of the state of a non-linear stochastic system from a set of indirect noisy measurements is a problem encountered in several fields of science. The particle filter and the ensemble Kalman filter are both used to get sub-optimal solutions of Bayesian inference problems, particularly for high-dimensional non-Gaussian and non-linear models. Both are essentially Monte Carlo techniques that compute their results using a set of estimated trajectories of the variable to be monitored. It has been shown that in a linear and Gaussian environment, solutions obtained from both these filters converge to the optimal solution obtained by the Kalman Filter. However, it is of interest to explore how the two filters compare to each other in basic methodology and construction, especially due to the similarity between them. In this work, we take up a specific problem of Bayesian inference in a restricted framework and compare analytically the results obtained from the particle filter and the ensemble Kalman filter. We show that for the chosen model, under certain assumptions, the two filters become methodologically analogous as the sample size goes to infinity.

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Les problèmes aux valeurs et fonctions propres surviennent fréquemment dans la théorie et dans les applications des processus stochastiques. Cependant quelques-uns seulement admettent une solution explicite; la résolution est alors généralement obtenue par la théorie généralisée de Sturm-Liouville pour les opérateurs différentiels. Les problèmes plus généraux ne peuvent pas être résolus sous une forme fermée et le sujet de cette thèse est l'analyse spectrale asymptotique des processus gaussiens fractionnaires et ses applications. Dans la première partie, nous développons une méthodologie pour l'analyse spectrale des opérateurs de covariance de type fractionnaire, correspondant à une famille importante de processus, incluant le processus fractionnaire d'Ornstein-Uhlenbeck, le mouvement brownien fractionnaire intégré et le mouvement brownien fractionnaire mixte. Nous obtenons des approximations asymptotiques du second ordre pour les valeurs propres et les fonctions propres. Au chapitre 2, nous considérons le problème aux valeurs et fonctions propres pour l'opérateur de covariance des ponts gaussiens. Nous montrons comment l'asymptotique spectrale d'un pont peut être dérivée de celle de son processus de base, en prenant comme exemple le cas du pont brownien fractionnaire. Dans la dernière partie, nous considérons trois applications représentatives de la théorie développée: le problème de filtrage des signaux gaussiens fractionnaires dans le bruit blanc, le problème de grande déviation pour le processus d'Ornstein-Uhlenbeck gouverné par un mouvement brownien fractionnaire mixte et probabilités des petites boules pour les processus gaussiens fractionnaires. / Eigenproblems frequently arise in theory and applications of stochastic processes, but only a few have explicit solutions. Those which do are usually solved by reduction to the generalized Sturm-Liouville theory for differential operators.The more general eigenproblems are not solvable in closed form and the subject of this thesis is the asymptotic spectral analysis of the fractional Gaussian processes and its applications.In the first part, we develop methodology for the spectral analysis of the fractional type covariance operators, corresponding to an important family of processes that includes the fractional Ornstein-Uhlenbeck process, the integrated fractional Brownian motion and the mixed fractional Brownian motion. We obtain accurate second order asymptotic approximations for both the eigenvalues and the eigenfunctions. In Chapter 2 we consider the covariance eigenproblem for Gaussian bridges. We show how the spectral asymptotics of a bridge can bederived from that of its base process, considering, as an example, the case of the fractional Brownian bridge. In the final part we consider three representative applications of the developed theory: filtering problem of fractional Gaussian signals in white noise, large deviation properties of the maximum likelihood drift parameter estimator for the Ornstein-Uhlenbeck process driven by mixed fractional Brownian motion and small ball probabilities for the fractional Gaussian processes.

In this thesis two different problems in distributed sensor networks are considered. Part I involves optimal quantiser design for decentralised estimation of a two-state hidden Markov model with dual sensors. The notion of optimality for quantiser design is based on minimising the probability of error in estimating the hidden Markov state. Equations for the filter error are derived for the continuous (unquantised) sensor outputs (signals), which are used to benchmark the performance of the quantisers. Minimising the probability of filter error to obtain the quantiser breakpoints is a difficult problem therefore an alternative method is employed. The quantiser breakpoints are obtained by maximising the mutual information between the quantised signals and the hidden Markov state. This method is known to work well for the single sensor case. Cases with independent and correlated noise across the signals are considered. The method is then applied to Markov processes with Gaussian signal noise, and further investigated through simulation studies. Simulations involving both independent and correlated noise across the sensors are performed and a number of interesting new theoretical results are obtained, particularly in the case of correlated noise. In Part II, the focus shifts to the detection of faults in helicopter transmission systems. The aim of the investigation is to determine whether the acoustic signature can be used for fault detection and diagnosis. To investigate this, statistical change detection algorithms are applied to acoustic vibration data obtained from the main rotor gearbox of a Bell 206 helicopter, which is run at high load under test conditions.