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.

Stuttgart, Univ., Diss., 2006. / Druckausg. beim VDI-Verl., Düsseldorf als: Fortschrittberichte / VDI : Reihe 8 ; Nr. 1125 erschienen.

This thesis is focused on the L1 regression, a possible alternative to the ordinary least squares regression. L1 regression replaces the least squares estimation with the least absolute deviations estimation, thus generalizing the sample median in the linear regres- sion model. Unlike the ordinary least squares regression, L1 regression enables loosening of certain assumptions and leads to more robust estimates. Fundamental theoretical re- sults, including the asymptotic distribution of regression coefficient estimates, hypothesis testing, confidence intervals and confidence regions, are derived. This method is then compared to the ordinary least squares regression in a simulation study, with a focus on heavy-tailed distributions and the possible presence of outlying observations. 1

This thesis aims to simultaneously minimize function error and model complexity for data fusion via the Choquet integral (CI). The CI is a generator function, i.e., it is parametric and yields a wealth of aggregation operators based on the specifics of the underlying fuzzy measure. It is often the case that we desire to learn a fusion from data and the goal is to have the smallest possible sum of squared error between the trained model and a set of labels. However, we also desire to learn as “simple’’ of solutions as possible. Herein, L1-norm regularization of a lexicographically encoded capacity vector relative to the CI is explored. The impact of regularization is explored in terms of what capacities and aggregation operators it induces under different common and extreme scenarios. Synthetic experiments are provided in order to illustrate the propositions and concepts put forth.

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.

O modelo de regressão linear com erros na família de distribuições t-assimétrica, que contempla as distribuições normal, t-Student e normal assimétrica como casos particulares, tem sido considerado uma alternativa robusta ao modelo normal. Para concluir qual modelo é, de fato, mais robusto, é importante ter um método tanto para identificar uma observação como discrepante quanto aferir a influência que esta observação terá em nossas estimativas. Nos modelos de regressão bayesianos, uma das medidas de identificação de observações discrepantes mais conhecidas é a conditional predictive ordinate (CPO). Analisamos a influência dessas observações nas estimativas tanto de forma global, isto é, no vetor completo de parâmetros do modelo quanto de forma marginal, apenas nos parâmetros regressores. Consideramos a norma L1 e a divergência Kullback-Leibler como medidas de influência das observações nas estimativas dos parâmetros. Além disso, encontramos as distribuições condicionais completas de todos os modelos para o uso do algoritmo de Gibbs obtendo, assim, amostras da distribuição a posteriori dos parâmetros. Tais amostras são utilizadas no calculo do CPO e das medidas de divergência estudadas. A principal contribuição deste trabalho é obter as medidas de influência global e marginal calculadas para os modelos t-Student, normal assimétrico e t-assimétrico. Na aplicação em dados reais originais e contaminados, observamos que, em geral, o modelo t-Student é uma alternativa robusta ao modelo normal. Por outro lado, o modelo t-assimétrico não é, em geral, uma alternativa robusta ao modelo normal. A capacidade de robustificação do modelo t-assimétrico está diretamente ligada à posição do resíduo do ponto discrepante em relação a distribuição dos resíduos. / The linear regression model with errors in the skew-t family, which includes the normal, Student-t and skew normal distributions as particular cases, has been considered as a robust alternative to the normal model. To conclude which model is in fact more robust its important to have a method to identify an observation as outlier, as well as to assess the influence of this observation in the estimates. In bayesian regression models, one of the most known measures to identify an outlier is the conditional predictive ordinate (CPO). We analyze the influence of these observations on the estimates both in a global way, that is, in the complete parameter vector of the model and in a marginal way, only in the regressor parameters. We consider the L1 norm and the Kullback-Leibler divergence as influence measures of the observations on the parameter estimates. Using the bayesian approach, we find the complete conditional distributions of all the models for the usage of the Gibbs sampler thus obtaining samples of the posterior distribution of the parameters. These samples are used in the calculation of the CPO and the studied divergence measures. The major contribution of this work is to present the global and marginal influence measures calculated for the Student-t, skew normal and skew-t models. In the application on original and contaminated real data, we observed that in general the Student-t model is a robust alternative to the normal model. However, the skew-t model is not a robust alternative to the normal model. The robustification capability of the skew-t model is directly linked to the position of the residual of the outlier in relation to the distribution of the residuals.

Afin d'améliorer la sûreté (dose plus faible) et la productivité (acquisition plus rapide) du système de la tomographie par rayons X (CT), nous cherchons à reconstruire une image de haute qualitée avec un faible nombre de projections. Les algorithmes classiques ne sont pas adaptés à cette situation et la reconstruction est instable et perturbée par des artefacts. L'approche "Compressed Sensing" (CS) fait l'hypothèse que l'image inconnue est "parcimonieuse" ou "compressible", et la reconstruit via un problème d'optimisation (minimisation de la norme TV/L1) en promouvant la parcimonie. Pour appliquer le CS en CT, en utilisant le pixel/voxel comme base de representation, nous avons besoin d'une transformée parcimonieuse, et nous devons la combiner avec le "projecteur du rayon X" appliqué sur une image pixelisée. Dans cette thèse, nous avons adapté une base radiale de famille Gaussienne nommée "blob" à la reconstruction CT par CS. Elle a une meilleure localisation espace-fréquentielle que le pixel, et des opérations comme la transformée en rayons-X, peuvent être évaluées analytiquement et sont facilement parallélisables (sur plateforme GPU par exemple). Comparé au blob classique de Kaisser-Bessel, la nouvelle base a une structure multi-échelle : une image est la somme des fonctions translatées et dilatées de chapeau Mexicain radiale. Les images médicales typiques sont compressibles sous cette base. Ainsi le système de representation parcimonieuse dans les algorithmes ordinaires de CS n'est plus nécessaire. Des simulations (2D) ont montré que les algorithmes TV/L1 existants sont plus efficaces et les reconstructions ont des meilleures qualités visuelles que par l'approche équivalente basée sur la base de pixel-ondelettes. Cette nouvelle approche a également été validée sur des données expérimentales (2D), où nous avons observé que le nombre de projections en général peut être réduit jusqu'à 50%, sans compromettre la qualité de l'image. / To improve the safety (lower dose) and the productivity (faster acquisition) of an X-ray CT system, we want to reconstruct a high quality image from a small number of projections. The classical reconstruction algorithms generally fail since the reconstruction procedure is unstable and the reconstruction suffers from artifacts. The "Compressed Sensing" (CS) approach supposes that the unknown image is in some sense "sparse" or "compressible", and reoncstructs it through a non linear optimization problem (TV/$llo$ minimization) by enhancing the sparsity. Using the pixel/voxel as basis, to apply CS framework in CT one usually needs a "sparsifying" transform, and combine it with the "X-ray projector" applying on the pixel image. In this thesis, we have adapted a "CT-friendly" radial basis of Gaussian family called "blob" to the CS-CT framework. It have better space-frequency localization properties than the pixel, and many operations, such as the X-ray transform, can be evaluated analytically and are highly parallelizable (on GPU platform). Compared to the classical Kaisser-Bessel blob, the new basis has a multiscale structure: an image is the sum of dilated and translated radial Mexican hat functions. The typical medical objects are compressible under this basis, so the sparse representation system used in the ordinary CS algorithms is no more needed. Simulations (2D) show that the existing TV/L1 algorithms are more efficient and the reconstructions have better visual quality than the equivalent approach based on the pixel/wavelet basis. The new approach has also been validated on experimental data (2D), where we have observed that the number of projections in general can be reduced to about 50%, without compromising the image quality.

O modelo de regressão linear com erros na família de distribuições t-assimétrica, que contempla as distribuições normal, t-Student e normal assimétrica como casos particulares, tem sido considerado uma alternativa robusta ao modelo normal. Para concluir qual modelo é, de fato, mais robusto, é importante ter um método tanto para identificar uma observação como discrepante quanto aferir a influência que esta observação terá em nossas estimativas. Nos modelos de regressão bayesianos, uma das medidas de identificação de observações discrepantes mais conhecidas é a conditional predictive ordinate (CPO). Analisamos a influência dessas observações nas estimativas tanto de forma global, isto é, no vetor completo de parâmetros do modelo quanto de forma marginal, apenas nos parâmetros regressores. Consideramos a norma L1 e a divergência Kullback-Leibler como medidas de influência das observações nas estimativas dos parâmetros. Além disso, encontramos as distribuições condicionais completas de todos os modelos para o uso do algoritmo de Gibbs obtendo, assim, amostras da distribuição a posteriori dos parâmetros. Tais amostras são utilizadas no calculo do CPO e das medidas de divergência estudadas. A principal contribuição deste trabalho é obter as medidas de influência global e marginal calculadas para os modelos t-Student, normal assimétrico e t-assimétrico. Na aplicação em dados reais originais e contaminados, observamos que, em geral, o modelo t-Student é uma alternativa robusta ao modelo normal. Por outro lado, o modelo t-assimétrico não é, em geral, uma alternativa robusta ao modelo normal. A capacidade de robustificação do modelo t-assimétrico está diretamente ligada à posição do resíduo do ponto discrepante em relação a distribuição dos resíduos. / The linear regression model with errors in the skew-t family, which includes the normal, Student-t and skew normal distributions as particular cases, has been considered as a robust alternative to the normal model. To conclude which model is in fact more robust its important to have a method to identify an observation as outlier, as well as to assess the influence of this observation in the estimates. In bayesian regression models, one of the most known measures to identify an outlier is the conditional predictive ordinate (CPO). We analyze the influence of these observations on the estimates both in a global way, that is, in the complete parameter vector of the model and in a marginal way, only in the regressor parameters. We consider the L1 norm and the Kullback-Leibler divergence as influence measures of the observations on the parameter estimates. Using the bayesian approach, we find the complete conditional distributions of all the models for the usage of the Gibbs sampler thus obtaining samples of the posterior distribution of the parameters. These samples are used in the calculation of the CPO and the studied divergence measures. The major contribution of this work is to present the global and marginal influence measures calculated for the Student-t, skew normal and skew-t models. In the application on original and contaminated real data, we observed that in general the Student-t model is a robust alternative to the normal model. However, the skew-t model is not a robust alternative to the normal model. The robustification capability of the skew-t model is directly linked to the position of the residual of the outlier in relation to the distribution of the residuals.