To reduce cost, many digital cameras use a single sensor array instead of using three arrays for the red, green and blue. Thus at each pixel location only the red, green or blue intensity value is available. And to generate a complete color image, the camera must estimate the missing two values at each pixel location .Color filter arrays are used to capture only one portion of the spectrum (Red, Green or Blue) at each location. Various arrangements of the Color Filter Array (CFA) are possible, but the Bayer array is the most commonly used arrangement and we will deal exclusively with the Bayer array in this thesis. Since each of the three colors channels are effectively downsampled, it leads to aliasing artifacts. This thesis will analyze the effects of aliasing in the frequency- domain and present a method to reduce the deterioration in image quality due to aliasing artifacts. Two reference algorithms, AH-POCS (Adams and Hamilton - Projection Onto Convex Sets) and Adaptive Homogeneity-Directed interpolation, are discussed in de- tail. Both algorithms use the assumption that there is high correlation in the high- frequency regions to reduce aliasing. AH-POCS uses alias cancellation technique to reduce aliasing in the red and blue images, while the Adaptive Homogeneity-Directed interpolation algorithm is an edge-directed algorithm. We present here an algorithm that combines these two techniques and provides a better result on average when compared to the reference algorithms.

La modélisation mathématique est un outil largement employé dans plusieurs disciplines des sciences appliquées. En hydrologie, en biologie, en économie ainsi que d'autres domaines des sciences naturelles, sociales et humaines, le recours à la modélisation mathématique est une démarche de plus en plus fréquente. Par exemple, en hydrologie, plusieurs modèles mathématiques sont conçus pour décrire ou prédire la relation existante entre les hauteurs d'eau et les débits des rivières. Dans le cadre de cette thèse nous nous sommes intéressés au développement de nouveaux modèles permettant de modéliser les phénomènes de croissance qui nécessitent la présence d'une asymptote linéaire croissante ou curviligne. Pour atteindre cet objectif, l'idée de base a été d'utiliser quelques modèles parmi les plus répandus en pratique et de les modifier judicieusement (et simplement) de façon à introduire une asymptote soit linéaire soit curviligne tout en conservant leur unique point d'inflexion. La modification que nous avons introduite conserve aussi le caractère simple et continue de ces modèles ainsi que la forme lisse et croissante de leurs courbes. Nous obtenons ainsi des modèles qui répondent aux besoins de la modélisation lorsque les modèles standards échouent.

ITC/USA 2008 Conference Proceedings / The Forty-Fourth Annual International Telemetering Conference and Technical Exhibition / October 27-30, 2008 / Town and Country Resort & Convention Center, San Diego, California / In this paper, we propose a highly precise and fast digital image stabilization technique based on the control grid interpolation. To obtain more stable video sequence than the one from other existing DIS techniques, the small instability should be removed in as small accuracy with sub-pixel. Experimental results show that the proposed digital image stabilizer gives considerable improvement in the sense of computational complexity and the performance of stabilizing compared to conventional DIS techniques.

In the recent decades the Fluid-Structure Interaction (FSI) problem has been of great interest to many researchers and a variety of methods have been proposed for its numerical simulation. As FSI simulation is a multi-discipline and a multi-physics problem, its full simulation consists of many details and sub-procedures. On the other hand, reliable FSI simulations are required in various applications ranging from hemo-dynamics and structural engineering to aero-elasticity. In hemo-dynamics an incompressible fluid is coupled with a flexible structure with similar density (e.g. blood in arteries). In aero-elasticity a compressible fluid interacts with a stiff structure (e.g. aircraft wing) or an incompressible flow is coupled with a very light structure (e.g. Parachute or sail), whereas in some other engineering applications an incompressible flow interacts with a flexible structure with large displacement (e.g. oil risers in offshore industries). Therefore, various FSI models are employed to simulate a variety of different applications. An initial vital step to conduct an accurate FSI simulation is to perform a study of the physics of the problem which would be the main criterion on which the full FSI simulation procedure will then be based. In this thesis, interaction of an incompressible fluid flow at low Reynolds number with a flexible circular cylinder in two dimensions has been studied in detail using some of the latest published methods in the literature. The elements of procedures have been chosen in a way to allow further development to simulate the interaction of an incompressible fluid flow with a flexible oil riser with large displacement in three dimensions in future. To achieve this goal, a partitioned approach has been adopted to enable the use of existing structural codes together with an Immersed Boundary (IB) method which would allow the modelling of large displacements. A direct forcing approach, interpolation / reconstruction, type of IB is used to enforce the moving boundary condition and to create sharp interfaces with the possibility of modelling in three dimensions. This provides an advantage over the IB continuous forcing approach which creates a diffused boundary. And also is considered as a preferred method over the cut cell approach which is very complex in three dimensions with moving boundaries. Different reconstruction methods from the literature have been compared with the newly proposed method. The fluid governing equation is solved only in the fluid domain using a Cartesian grid and an Eulerian approach while the structural analysis was performed using Lagrangian methods. This method avoids the creation of secondary fluid domains inside the solid boundary which occurs in some of the IB methods. In the IB methods forces from the Eulerian flow field are transferred onto the Lagrangian marker points on the solid boundary and the displacement and velocities of the moving boundary are interpolated in the flow domain to enforce no-slip boundary conditions. Various coupling methods from the literature were selected and improved to allow modelling the interface and to transfer the data between fluid and structure. In addition, as an alternative method to simulate FSI for a single object in the fluid flow as suggested in the literature, the moving frame of reference method has been applied for the first time in this thesis to simulate Fluid-Structure interaction using an IB reconstruction approach. The flow around a cylinder in two dimensions was selected as a benchmark to validate the simulation results as there are many experimental and analytical results presented in the literature for this specific case.

International Telemetering Conference Proceedings / October 21, 2002 / Town & Country Hotel and Conference Center, San Diego, California / With the purpose of testing the performance of GPS receivers, a GPS signal simulator is needed that can emulate the real GPS signals under all kinds of the conditions. This paper analyzes the single channel and multi-channel GPS signals’ characters in time domain and frequency domain, and discusses a mathematic model of the twelve-channel GPS simulator. In order to reduce the difficulties of the hardware design, this model is designed to provide the IF signal directly by applying the idea of “software radio”and the theory of interpolation. Simulation results with SystemView software demonstrate the feasibility of the system scheme. A practical hardware design of this system is described.

Thesis (DSc (Mathematical Sciences))--University of Stellenbosch, 2005. / Subdivision is an important iterative technique for the efficient generation of curves and surfaces in geometric modelling. The convergence of a subdivision scheme is closely connected to the existence of a corresponding refinable function. In turn, such a refinable function can be used in the multi-resolutional construction method for wavelets, which are applied in many areas of signal analysis.

Subdivision surfaces are capable of modeling and representing complex shapes of arbi-trary topology. However, methods on how to build the control mesh of a complex surfaceare not studied much. Currently, most meshes of complicated objects come from trian-gulation and simplification of raster scanned data points, like the Stanford 3D ScanningRepository. This approach is costly and leads to very dense meshes.Subdivision surface based one-piece representation means to represent the final objectin a design process with only one subdivision surface, no matter how complicated theobject's topology or shape. Hence the number of parts in the final representation isalways one.In this dissertation we present necessary mathematical theories and geometric algo-rithms to support subdivision surface based one-piece representation. First, an explicitparametrization method is presented for exact evaluation of Catmull-Clark subdivisionsurfaces. Based on it, two approaches are proposed for constructing the one-piece rep-resentation of a given object with arbitrary topology. One approach is to construct theone-piece representation by using the interpolation technique. Interpolation is a naturalway to build models, but the fairness of the interpolating surface is a big concern inprevious methods. With similarity based interpolation technique, we can obtain bet-ter modeling results with less undesired artifacts and undulations. Another approachis through performing Boolean operations. Up to this point, accurate Boolean oper-ations over subdivision surfaces are not approached yet in the literature. We presenta robust and error controllable Boolean operation method which results in a one-piecerepresentation. Because one-piece representations resulting from the above two methodsare usually dense, error controllable simplification of one-piece representations is needed.Two methods are presented for this purpose: adaptive tessellation and multiresolutionanalysis. Both methods can significantly reduce the complexity of a one-piece represen-tation and while having accurate error estimation.A system that performs subdivision surface based one-piece representation was im-plemented and a lot of examples have been tested. All the examples show that our ap-proaches can obtain very good subdivision based one-piece representation results. Eventhough our methods are based on Catmull-Clark subdivision scheme, we believe they canbe adapted to other subdivision schemes as well with small modifications.

L'adaptation de maillage pour l'approximation des fonctions par éléments finis permet d'adapter localement la résolution en la raffinant dans les lieux de variations rapides de la fonction. Cette méthode intervient dans de nombreux domaines du calcul scientifique. L'utilisation de triangles anisotropes permet d'améliorer l'efficacité du maillage en introduisant des triangles longs et fins épousant notamment les directions des courbes de discontinuité. Etant donnée une norme d'intérêt et une fonction f à approcher, nous formulons le problème de l'adaptation optimale de maillage, comme la minimisation de l'erreur d'approximation par éléments finis de degré k donné parmi toutes les triangulations (potentiellement anisotropes) de cardinalité donnée N du domaine de définition de f. Nous étudions ce problème sous l'angle des quatre questions ci dessous: I. Comment l'erreur d'approximation se comporte-t-elle dans le régime asymptotique où le nombre N de triangles tend vers l'infini, lorsque f est une fonction suffisamment régulière? II. Quelles classes de fonctions gouvernent la vitesse de décroissance de l'erreur d'approximation lorsque N augmente, et sont en ce sens naturellement liées au problème d'adaptation optimale de maillage? III. Ce problème d'optimisation, qui porte sur les triangulations de cardinalité donnée N, peut-il être remplacé par un problème équivalent portant sur un objet continu? IV. Est-il possible de construire une suite quasi-optimale de triangulations en utilisant une procédure hiérarchique de raffinement?

<p>To counter radio signal reconnaissance, an efficient way of covert communication is to use subsecond duration burst transmissions in the congested HF band. Against this background, the present thesis treats fast direction finding (DF) using antenna arrays with known response only in a few calibration directions. In such scenarios the known method of array mapping (interpolation) may be used to transform the output data vectors from the existing array onto the corresponding output vectors of another (virtual) array that is mathematically defined and optimally chosen. But in signal reconnaissance the emitters are initially unknown and the mapping matrix must be designed as a compromise over a wide sector of DOAs. This compromise may result in large DOA estimate errors, both deterministic and random. Analyzing, analytically describing, and minimizing these DOA errors, is the main theme of the present thesis. The first part of the thesis analyzes the deterministic mapping errors, the DOA estimate bias, that is caused by dissimilarity between the two array geometries. It is shown that in a typical signal reconnaissance application DOA estimate bias can dominate over DOA estimate variance. Using a Taylor series expansion of the DOA estimator cost function an analytical expression for the bias is derived and a first order zero bias condition is identified. This condition is general, estimator independent, and can be applied to any type of data pre-processing. A design algorithm for the mapping matrix is thereafter presented that notably reduces mapped DOA estimate bias. A special version is also given with the additional property of reducing the higher order Taylor terms and thus the residual bias. Simulations demonstrate a bias reduction factor exceeding 100 in some scenarios. A version based on signal subspace mapping rather than array manifold mapping is also given. This version is of large practical interest since the mapping matrix can be designed directly from calibration data. In the second part of the thesis the derived bias minimization theory is extended into Mean Square Error (MSE) minimization, i.e. measurement noise is introduced. Expressions for DOA error variance and DOA MSE under general pre-processing are derived, and a design algorithm for the mapping matrix is formulated by which mapped DOA estimate MSE can be minimized. Simulations demonstrate improved robustness and performance for this algorithm, especially in low SNR scenarios. In the third and final part of the thesis the theoretical results are supported by experimental data. For an 8 element circular array mapped onto a virtual ULA across a 600 sector it is shown that the mapped DOA estimate errors can be suppressed down to the Cramér-Rao level.</p>

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