A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas. / Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.

A compressão de dados é uma área de muito interesse em termos computacionais devido à necessidade de armazená-los e transmiti-los. Em particular, a compressão de malhas possui grande interesse em função do crescimento de sua utilização em jogos tridimensionais e modelagens diversas. Nos últimos anos, uma nova teoria de aquisição e reconstrução de sinais foi desenvolvida, baseada no conceito de esparsidade na minimização da norma L1 e na incoerência do sinal, chamada Compressive Sensing (CS). Essa teoria possui algumas características marcantes, como a aleatoriedade de amostragem e a reconstrução via minimização, de modo que a própria aquisição do sinal é feita considerando somente os coeficientes significativos. Qualquer objeto que possa ser interpretado como um sinal esparso permite sua utilização. Assim, ao se representar esparsamente um objeto (sons, imagens) é possível aplicar a técnica de CS. Este trabalho verifica a viabilidade da aplicação da teoria de CS na compressão de malhas, de modo que seja possível um sensoreamento e representação compressivos na geometria de uma malha. Nos experimentos realizados, foram utilizadas variações dos parâmetros de entrada e técnicas de minimização da Norma L1. Os resultados obtidos mostram que a técnica de CS pode ser utilizada como estratégia de compressão da geometria das malhas. / Data compression is an area of a major interest in computational terms due to the issues on storage and transmission. Particularly, mesh compression has wide usage due to the increase of its application in games and three-dimensional modeling. In recent years, a new theory of acquisition and reconstruction of signals was developed, based on the concept of sparsity and in the minimization of the L1 norm and the incoherency of the signal, called Compressive Sensing (CS). This theory has some remarkable features, such as random sampling and reconstruction by minimization, in a way that the signal acquisition is done by considering only its significant coefficients. Any object that can be interpreted as a sparse sign allows its use. Thus, representing an object sparsely (sounds, images), you can apply the technique of CS. This work explores the viability of CS theory on mesh compression, so that it is possible a representative and compressive sensing on the mesh geometry. In the performed experiments, different parameters and L1 Norm minimization strategies were used. The results show that CS can be used as a mesh geometry compression strategy.

The rapid developments in the sensor and its related technology have made automation possible in many processes in diverse fields. Also sensor-based fault diagnosis and quality improvements have been made possible. These tasks depend highly on the sensor network for the accurate measurements. The two major problems that affect the reliability of the sensor system/network are sensor failures and sensor anomalies. The usage of redundant sensors offers some tolerance against these two problems. Hence the redundancy analysis of the sensor system is essential in order to clearly know the robustness of the system against these two problems. The degree of sensor redundancy defined in this thesis is closely tied with the fault-tolerance of the sensor network and can be viewed as a parameter related to the effectiveness of the sensor system design. In this thesis, an efficient algorithm to determine the degree of sensor redundancy for linear sensor systems is developed. First the redundancy structure is linked with the matroid structure, developed from the design matrix, using the matroid theory. The matroid problem equivalent to the degree of sensor redundancy is developed and the mathematical formulation for it is established. The solution is obtained by solving a series of l1-norm minimization problems. For many problems tested, the proposed algorithm is more efficient than other known alternatives such as basic exhaustive search and bound and decomposition method. The proposed algorithm is tested on problem instances from the literature and wide range of simulated problems. The results show that the algorithm determines the degree of redundancy more accurately when the design matrix is dense than when it is sparse. The algorithm provided accurate results for most problems in relatively short computation times.

L'objectif de cette thèse est l'optimisation de la qualité perçue de la reproduction sonore par un système audio multicanal, dans un contexte de salle d'écoute domestique. Les travaux de recherche présentés s'articulent selon deux axes. Le premier concerne l'effet de salle, et plus particulièrement les aspects physiques et perceptifs liés aux premières réflexions d'une salle. Ces éléments sont décrits spécifiquement, et une expérience psychoacoustique a été menée afin d'étendre les données disponibles quant à leur perceptibilité, c'est à dire leur capacité à modifier la perception du son direct, que ce soit en termes de timbre ou de localisation. Les résultats mettent en évidence la dépendance du seuil en fonction du type de stimulus, ainsi que son évolution en fonction de la configuration spatiale de l'onde directe et de la réflexion. Pour une condition donnée, le seuil de perceptibilité est décrit comme une fonction de directivité dépendant de l'incidence de la réflexion.Le deuxième axe de travail concerne les méthodes de correction de l'effet de la salle de reproduction. Les méthodes numériques classiques sont d'abord étudiées. Leur principale lacune réside dans l'absence de prise en compte du rôle spécifique des propriétés temporelles et spatiales des première réflexions. Le travail de thèse se termine par la proposition d'une nouvelle méthode de correction utilisant un algorithme itératif de type FISTA modifié afin de prendre en compte la perceptibilité des réflexions. Le traitement est implémenté dans une représentation où l'information spatiale est analysée sur la base des harmoniques sphériques. / The goal of this Ph. D. thesis is to optimize the perceived quality of multichannel sound reproduction systems, in the context of a domestic listening room. The presented research work have been pursued in two different directions.The first deals with room effet, and more particularly with physical and perceptual aspects of first reflections within a room. These reflections are specifically described, and a psychoacoustical experiment have been carried out in order to extend the available data on their perceptibility, i.e. their potency in altering the perception of the direct sound, whether in its timbral or spatial features. Results exhibit the variation of the threshold depending on the type of stimulus, as well as on the spatial configuration of the direct sound and the reflection. For a given condition, the perceptibility threshold is given as a directivity function depending on the direction of incidence of the reflection.The second topic deals with room correction methods. Firstly, state-of-the art digital methods are investigated. Their main drawback is that they don't consider the specific impact of the temporal and spatial attributes of first reflections. A new correction method is therefore proposed. It uses an iterative algorithm, derivated from the FISTA method, in order to take into account the perceptibility of the reflections. All the processing is carried out in a spatial sound representation, where the spatial properties of the sound are analysed thanks to spherical harmonics.

This thesis presents compressive sensing algorithms that utilize system dynamics in the sparse signal recovery process. These dynamics may arise due to a time-varying signal, streaming measurements, or an adaptive signal transform. Compressive sensing theory has shown that under certain conditions, a sparse signal can be recovered from a small number of linear, incoherent measurements. The recovery algorithms, however, for the most part are static: they focus on finding the solution for a fixed set of measurements, assuming a fixed (sparse) structure of the signal. In this thesis, we present a suite of sparse recovery algorithms that cater to various dynamical settings. The main contributions of this research can be classified into the following two categories: 1) Efficient algorithms for fast updating of L1-norm minimization problems in dynamical settings. 2) Efficient modeling of the signal dynamics to improve the reconstruction quality; in particular, we use inter-frame motion in videos to improve their reconstruction from compressed measurements. Dynamic L1 updating: We present homotopy-based algorithms for quickly updating the solution for various L1 problems whenever the system changes slightly. Our objective is to avoid solving an L1-norm minimization program from scratch; instead, we use information from an already solved L1 problem to quickly update the solution for a modified system. Our proposed updating schemes can incorporate time-varying signals, streaming measurements, iterative reweighting, and data-adaptive transforms. Classical signal processing methods, such as recursive least squares and the Kalman filters provide solutions for similar problems in the least squares framework, where each solution update requires a simple low-rank update. We use homotopy continuation for updating L1 problems, which requires a series of rank-one updates along the so-called homotopy path. Dynamic models in video: We present a compressive-sensing based framework for the recovery of a video sequence from incomplete, non-adaptive measurements. We use a linear dynamical system to describe the measurements and the temporal variations of the video sequence, where adjacent images are related to each other via inter-frame motion. Our goal is to recover a quality video sequence from the available set of compressed measurements, for which we exploit the spatial structure using sparse representations of individual images in a spatial transform and the temporal structure, exhibited by dependencies among neighboring images, using inter-frame motion. We discuss two problems in this work: low-complexity video compression and accelerated dynamic MRI. Even though the processes for recording compressed measurements are quite different in these two problems, the procedure for reconstructing the videos is very similar.

Dans les maisons et bâtiments intelligents, il devient nécessaire de limiter l'intervention humaine sur le système énergétique, afin de fluctuer automatiquement l'énergie consommée par les appareils consommateurs. Pour cela, un système de mesure de la consommation électrique d'équipements est aussi nécessaire et peut être déployé de deux façons : intrusive ou non-intrusive. La première solution consiste à relever la consommation de chaque appareil, ce qui est inenvisageable à une grande échelle pour des raisons pratiques liées à l'entretien et aux coûts. Donc, la solution non-intrusive (NILM pour Non-Intrusive Load Monitoring), qui est capable d'identifier les différents appareils en se basant sur les signatures extraites d'une consommation globale, est plus prometteuse. Le problème le plus difficile des algorithmes NILM est comment discriminer les appareils qui ont la même caractéristique énergétique. Pour surmonter ce problème, dans cette thèse, nous proposons d'utiliser une information externe pour améliorer la performance des algorithmes existants. Les premières informations additionnelles proposées considèrent l'état précédent de chaque appareil comme la probabilité de transition d'état ou la distance de Hamming entre l'état courant et l'état précédent. Ces informations sont utilisées pour sélectionner l'ensemble le plus approprié des dispositifs actifs parmi toutes les combinaisons possibles. Nous résolvons ce problème de minimisation en norme l1 par un algorithme d'exploration exhaustive. Nous proposons également d'utiliser une autre information externe qui est la probabilité de fonctionnement de chaque appareil fournie par un réseau de capteurs sans fil (WSN pour Wireless Sensor Network) déployé dans le bâtiment. Ce système baptisé SmartSense, est différent de la solution intrusive car seul un sous-ensemble de tous les dispositifs est surveillé par les capteurs, ce qui rend le système moins intrusif. Trois approches sont appliquées dans le système SmartSense. La première approche applique une détection de changements de niveau sur le signal global de puissance consommé et les compare avec ceux existants pour identifier les dispositifs correspondants. La deuxième approche vise à résoudre le problème de minimisation en norme l1 avec les algorithmes heuristiques de composition Paréto-algébrique et de programmation dynamique. Les résultats de simulation montrent que la performance des algorithmes proposés augmente significativement avec la probabilité d'opération des dispositifs surveillés par le WSN. Comme il n'y a qu'un sous-ensemble de tous les appareils qui sont surveillés par les capteurs, ceux qui sont sélectionnés doivent satisfaire quelques critères tels qu'un taux d'utilisation élevé ou des confusions dans les signatures sélectionnées avec celles des autres. / In smart homes, human intervention in the energy system needs to be eliminated as much as possible and an energy management system is required to automatically fluctuate the power consumption of the electrical devices. To design such system, a load monitoring system is necessary to be deployed in two ways: intrusive or non-intrusive. The intrusive approach requires a high deployment cost and too much technical intervention in the power supply. Therefore, the Non-Intrusive Load Monitoring (NILM) approach, in which the operation of a device can be detected based on the features extracted from the aggregate power consumption, is more promising. The difficulty of any NILM algorithm is the ambiguity among the devices with the same power characteristics. To overcome this challenge, in this thesis, we propose to use an external information to improve the performance of the existing NILM algorithms. The first proposed additional features relate to the previous state of each device such as state transition probability or the Hamming distance between the current state and the previous state. They are used to select the most suitable set of operating devices among all possible combinations when solving the l1-norm minimization problem of NILM by a brute force algorithm. Besides, we also propose to use another external feature that is the operating probability of each device provided by an additional Wireless Sensor Network (WSN). Different from the intrusive load monitoring, in this so-called SmartSense system, only a subset of all devices is monitored by the sensors, which makes the system quite less intrusive. Two approaches are applied in the SmartSense system. The first approach applies an edge detector to detect the step-changes on the power signal and then compare with the existing library to identify the corresponding devices. Meanwhile, the second approach tries to solve the l1-norm minimization problem in NILM with a compositional Pareto-algebraic heuristic and dynamic programming algorithms. The simulation results show that the performance of the proposed algorithms is significantly improved with the operating probability of the monitored devices provided by the WSN. Because only part of the devices are monitored, the selected ones must satisfy some criteria including high using rate and more confusions on the selected patterns with the others.