Resumo: O multicaminho é um dos fenômenos que ocorre quando o sinal proveniente do Global Navigation Satellite System (GNSS) reflete em objetos localizados nas proximidades do levantamento e chega ao receptor via múltiplos caminhos. Geralmente, o receptor GNSS recebe além do sinal direto, também o sinal refletido, o qual é atrasado em relação ao sinal direto. Conseqüentemente, as medidas de pseudodistância (PD) e fase de batimento da onda portadora são rastreadas para um sinal composto, e não para o sinal direto, causando o erro do multicaminho. Esse efeito é uma fonte de erro significativa que ainda permanece como um desafio para a pesquisa, especialmente para o posicionamento relativo estático e cinemático em aplicações de alta precisão. Diferentemente dos demais erros, o multicaminho não é atenuado quando se formam as duplas diferenças (DD) em uma linha de base curta, por ser um efeito altamente dependente do local do levantamento. Pelo contrário, os erros de multicaminho podem aumentar no processo de dupla diferenciação. Nessa pesquisa foi proposta uma metodologia, viável em termos práticos e econômicos, capaz de detectar e corrigir o efeito do multicaminho nas observações de fase da onda portadora e PD L1 e/ou L2 para aplicações estáticas e cinemáticas, quer sejam pós-processadas ou em tempo real. Essa metodologia é baseada na Análise de Multirresolução (AMR) utilizando a Transformada de Wavelets (TW). A TW é aplicada para decompor as séries temporais dos resíduos das DDs do ajustamento em componentes de freqüências baixa e alta... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: GNSS-multipath is a phenomenon that occurs when the signal from Global Navigation Satellite System (GNSS) reflects on objects surrounding the survey environment and reaches the receiver antenna through multiple paths. Usually, the GNSS receiver also collects the reflected signal, which is delayed in relation to the direct one. Consequently, the pseudorange (code) and carrier phase measurements are tracked for a composed signal, and not for the direct signal, causing a multipath error. This effect is a significant error source that still remains as a challenge for the research, especially for static and kinematic relative positioning in high-precision applications. Differently from other errors sources, multipath is not attenuated when the double differences (DD) are formed in a short baseline, because this error is highly dependent upon the surrounding environment. On the contrary, multipath errors can even increase in the double differentiation process. In this research a feasible and economic methodology, able of detecting and correcting the multipath effect from the carrier phase and pseudorange L1 and/or L2 for static and kinematic applications, post-processed or in real time. This approach is based on the Multiresolution Analysis (MRA) using the Wavelet Transform (WT)... (Complete abstract click electronic access below) / Orientador: João Francisco Galera Monico / Coorientador: Aylton Pagamisse / Banca: Hélio Magalhães de Oliveira / Banca: Silvio Rogério Correia Freitas / Banca: Messias Meneguette Junior / Banca: Paulo de Oliveira Camargo / Doutor

Flows around immersed boundaries exhibit many complex, well defined and active dynamical structures. In fact, features such as shock waves, strong vorticity concentrations in shear layers, wakes, or boundary layer regions are critical elements in representing the dynamics of a flow field. In order to capture the correct kinematic and dynamic quantities associated with the fluid flows, one must be able to efficiently refine the computational mesh around areas containing high gradients of pressure, density, velocity, or other suitable flowfield variables that characterize distinct structures. Although there are techniques which utilize simple gradient-based Local Mesh Refinement (LMR) to adapt resolution selectively to capture structures in the flow, such methods lack the ability to refine structures based on the relative strengths and scales of structures that are presented in the flow. The inability to adequately define the strength and scale of structures typically results in the mesh being over-refined in regions of little consequence to the physical definition of the problem, under-refined in certain regions resulting in the loss of important features, or even the emergence of false features due to perturbations in the flowfield caused by unnecessary mesh refinement. On the other hand, significant user judgment is required to develop a "good enough" mesh for a given flow problem, so that important structures in the flowfield can be resolved. In order to overcome this problem, multiresolution techniques based on the wavelet transform are explored for feature identification and refinement. Properties and current uses of these functional transforms in fluid flow computations will be briefly discussed. A Multiresolution Transform (MRT) scheme is chosen for identifying coherent structures because of its ability to capture the scale and relative intensity of a structure, and its easy application on non-uniform meshes. The procedure used for implementation of the MRT on an octree/quadtree LMR mesh is discussed in detail, and techniques used for the identification and capture of jump discontinuities and scale information are also presented. High speed compressible flow simulations are presented for a number of cases using the described MRT LMR scheme. MRT based mesh refinement performance is analyzed and further suggestions are made for refinement parameters based on resulting refinement. The key contribution of this thesis is the identification of methods that lead to a robust, general (i.e. not requiring user-defined parameters) methodology to identify structures in compressible flows (shocks, slip lines, vertical patterns) and to direct refinement to adequately refine these structures. The ENO-MRT LMR scheme is shown to be a robust, automatic, and relatively inexpensive way of gaining accurate refinement of the major features contained in the flowfield.

In this thesis we will explore the theory behind wavelets. The main focus is on the discrete wavelet transform, although to reach this goal we will also introduce the discrete Fourier transform as it allow us to derive important properties related to wavelet theory, such as the multiresolution analysis. Based on the multiresolution it will be shown how the discrete wavelet transform can be formulated and show how it can be expressed in terms of a matrix. In later chapters we will see how the discrete wavelet transform can be generalized into two dimensions, and discover how it can be used in image processing.

Les schémas de subdivision sont largement utilisés pour la génération rapide de courbes ou de surfaces. Des développements récents ont produit des schémas variés, en particulier non-linéaires, non-interpolants ou non-homogènes.Pour pouvoir être utilisés en compression, analyse ou contrôle de données, ces schémas de subdivision doivent être incorporés dans une analyse multiresolution qui, imitant les analyses en ondelettes, fournit une décomposition multi-échelle d'un signal, d'une courbe ou d'une surface. Les ingrédients nécessaires à la définition d'une analyse multiresolution associée à un schéma de subdivision sont des schémas de décimation et de détails. Leur construction est facile quand le schéma de multiresolution est interpolant.Cette thèse est consacrée à la construction de schémas de décimation et de détails compatibles avec un schéma de subdivision le plus général possible. Nous commençons par une construction générique dans le cas d'opérateurs homogènes (mais pas interpolants) puis nous généralisons à des situations non-homogènes et non-linéaires. Nous construisons ainsi des analyses multiresolutions compatibles avec de nombreux schémas récemment développés. L'analyse des performances des analyses ainsi construitesest effectuée. Nous présentons des applications numériques en compression d'images. / Subdivision schemes are widely used for rapid curve or surface generation. Recent developments have produced various schemes, in particular non-linear, non-interpolatory or non-uniform.To be used in compression, analysis or control of data, subdivision schemes should be incorporated in a multiresolution analysis that, mimicking wavelet analyses, provides a multi-scale decomposition of a signal, a curve, or a surface. The ingredients needed to define a multiresolution analysis associated with a subdivision scheme are decimation scheme and detail operators. Their construction is straightforward when the multiresolution scheme is interpolatory.This thesis is devoted to the construction of decimation schemes and detail operators compatible with general subdivision schemes. We start with a generic construction in the uniform (but not interpolatory) case and then generalize to non-uniform and non-linear situations. Applying these results, we build multiresolution analyses that are compatible with many recently developed schemes. Analysis of the performances of the constructed analyses is carried out. We present numerical applications in image compression.

This paper considers some numerical schemes for the approximate solution of conservation laws and various wavelet methods are reviewed. This is followed by the construction of wavelet spaces based on a polynomial framework for the approximate solution of conservation laws. Construction of a representation of the approximate solution in terms of an entropy satisfying Multiresolution Analysis (MRA) is defined. Finally, a proof of convergence of the approximate solution of conservation laws using the characterization provided by the basis functions in the MRA will be given.

Spaceborne sensors, which collect imagery of the Earth in various spectral bands, are limited by the data transmission rates. As a result the multispectral bands are transmitted at a lower resolution and only the panchromatic band is transmitted at its full resolution. The information contained in the multispectral bands is an invaluable tool for land use mapping, urban feature extraction, etc. However, the limited spatial resolution reduces the appeal and value of this information. Pan sharpening techniques enhance the spatial resolution of the multispectral imagery by extracting the high spatial resolution of the panchromatic band and adding it to the multispectral images. There are many different pan sharpening methods available like the ones based on the Intensity-Hue-Saturation and the Principal Components Analysis transformation. But these methods cause heavy spectral distortion of the multispectral images. This is a drawback if the pan sharpened images are to be used for classification based applications. In recent years, multiresolution based techniques have received a lot of attention since they preserve the spectral fidelity in the pan sharpened images. Many variations of the multiresolution based techniques exist. They differ based on the transform used to extract the high spatial resolution information from the images and the rules used to synthesize the pan sharpened image. The superiority of many of the techniques has been demonstrated by comparing them with fairly simple techniques like the Intensity-Hue-Saturation or the Principal Components Analysis. Therefore there is much uncertainty in the pan sharpening community as to which technique is the best at preserving the spectral fidelity. This research investigates these variations in order to find an answer to this question. An important parameter of the multiresolution based methods is the number of decomposition levels to be applied. It is found that the number of decomposition levels affects both the spatial and spectral quality of the pan sharpened images. The minimum number of decomposition levels required to fuse the multispectral and panchromatic images was determined in this study for image pairs with different resolution ratios and recommendations are made accordingly.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal.

Thèse numérisée par la Division de la gestion de documents et des archives de l'Université de Montréal

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Mon travail de thèse consiste en la mise en place d'une méthode de reconstruction 3D. Les objets à reconstruire sont des petits corps du système solaire qui ont été observée dans le domaine visible par des sondes lors de missions spatiales. La méthode proposée (appelée photoclinométrie par déformation) consiste à déformer un maillage jusqu'à ce que les images synthétiques de ce maillage correspondent aux images observées, ceci s'effectue au sein d'une boucle d'optimisation. Cette méthode nécessitant un maillage de départ proche de la solution souhaitée, nous avons implémenter cette méthode au sein d'un schéma multirésolution (multirésolution photoclinométrie par déformation) permettant d'obtenir une reconstruction sans apriori de forme. Cependant cette méthode ne permet pas d'obtenir de modèles contenant des millions de facettes. Une troisième méthode a donc été développé pour pallier ce problème, elle consiste à découper le maillage en différents morceaux et à appliquer la méthode multirésolution photoclinométrie par déformation à chacun de ces morceaux. Par fusion de ces morceaux, on arrive ainsi à obtenir des maillages de plusieurs millions de facettes (modèle haute résolution). Ces méthodes ont été testées avec la reconstruction des deux astéroïdes (Steins and lutetia) survolé par la sonde Rosetta de l'Agence Spatiale Européenne (ESA). / My PhD work consists in the establishment of a method of 3D reconstruction. Studied objects are small solar system bodies that have been observed in the visible range by sensors during space missions. The proposed method (called photoclinometry by deformation ) consists in deforming a mesh until the synthetic images of the mesh correspond to the observed ones, this is done in an optimization loop . This method requires an initial mesh close to the desired solution. We implement this method in a multiresolution scheme (multiresolution photoclinometry by deformation) to obtain a reconstruction without an apriori shape . However, this method does not allow models containing millions of facets . A third method has been developed to overcome this problem, it consists in cutting the mesh into different pieces and apply the multiresolution method photoclinometry by deforming to each of these pieces . By merging these pieces , we obtain meshes of several millions facets (high resolution model). These methods have been tested by reconstructing the two asteroids (Steins and lutetia) flown-by the Rosetta spacecraft of the European Space Agency (ESA).