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Thesis (M.S.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains ix, 76 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 71-76).

Thesis (M.S.)--University of Texas at El Paso, 2009. / Title from title screen. Vita. CD-ROM. Includes bibliographical references. Also available online.

Typescript. Includes vita and abstract. Includes bibliographical references (leaves 98-99). Also available online in Scholars' Bank; and in ProQuest, free to University of Oregon users.

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xvii, 158 p.; also includes graphics (some col.). Includes bibliographical references (p. 150-158). Available online via OhioLINK's ETD Center

Philosophiae Doctor - PhD / In this thesis, we design and implement a class of numerical methods (based on integral transforms) to solve PDEs for pricing a variety of financial derivatives. Our approach is based on spectral discretization of the spatial (asset) derivatives and the use of inverse Laplace transforms to solve the resulting problem in time. The conventional spectral methods are further modified by using piecewise high order rational interpolants on the Chebyshev mesh within each sub-domain with the boundary domain placed at the strike price where the discontinuity is located. The resulting system is then solved by applying Laplace transform method through deformation of a contour integral. Firstly, we use this approach to price plain vanilla options and then extend it to price options described by a jump-diffusion model, barrier options and the Heston’s volatility model. To approximate the integral part in the jump-diffusion model, we use the Gauss-Legendre quadrature method. Finally, we carry out extensive numerical simulations to value these options and associated Greeks (the measures of sensitivity). The results presented in this thesis demonstrate the spectral accuracy and efficiency of our approach, which can therefore be considered as an alternative approach to price these class of options.

Les codeurs vidéo état de l’art utilisent des transformées pour assurer une représentation compacte du signal. L’étape de transformation constitue le domaine dans lequel s’effectue la compression, pourtant peu de variabilité dans les types de transformations est constatée dans les systèmes de codage vidéo normalisés : souvent, une seule transformée est considérée, habituellement la transformée en cosinus discrète (DCT). Récemment, d’autres transformées ont commencé à être considérées en complément de la DCT. Par exemple, dans le dernier standard de compression vidéo, nommé HEVC (High Efficiency Video Coding), les blocs de taille 4x4 peuvent utiliser la transformée en sinus discrète (DST), de plus, il est également possible de ne pas les transformer. Ceci révèle un intérêt croissant pour considérer une pluralité de transformées afin d’augmenter les taux de compression. Cette thèse se concentre sur l’extension de HEVC au travers de l’utilisation de multiples transformées. Après une introduction générale au codage vidéo et au codage par transformée, une étude détaillée de deux méthodes de construction de transformations est menée : la transformée de Karhunen Loève (KLT) et une transformée optimisée en débit et distorsion sont considérées. Ces deux méthodes sont comparées entre-elles en substituant les transformées utilisées par HEVC. Une expérimentation valide la pertinence des approches. Un schéma de codage qui incorpore et augmente l’utilisation de multiples transformées est alors introduit : plusieurs transformées sont mises à disposition de l’encodeur, qui sélectionne celle qui apporte le meilleur compromis dans le plan débit distorsion. Pour ce faire, une méthode de construction qui permet de concevoir des systèmes comportant de multiples transformations est décrite. Avec ce schéma de codage, le débit est significativement réduit par rapport à HEVC, tout particulièrement lorsque les transformées sont nombreuses et complexes à mettre en oeuvre. Néanmoins, ces améliorations viennent au prix d’une complexité accrue en termes d’encodage, de décodage et de contrainte de stockage. En conséquence, des simplifications sont considérées dans la suite du document, qui ont vocation à limiter l’impact en réduction de débit. Une première approche est introduite dans laquelle des transformées incomplètes sont motivées. Les transformations de ce type utilisent un seul vecteur de base, et sont conçues pour travailler de concert avec les transformations de HEVC. Cette technique est évaluée et apporte une réduction de complexité significative par rapport au précédent système, bien que la réduction de débit soit modeste. Une méthode systématique, qui détermine les meilleurs compromis entre le nombre de transformées et l’économie de débit est alors définie. Cette méthode utilise deux types différents de transformée : basés sur des transformées orthogonales séparables et des transformées trigonométriques discrètes (DTT) en particulier. Plusieurs points d’opération sont présentés qui illustrent plusieurs compromis complexité / gain en débit. Ces systèmes révèlent l’intérêt de l’utilisation de transformations multiples pour le codage vidéo. / State of the art video codecs use transforms to ensure a compact signal representation. The transform stage is where compression takes place, however, little variety is observed in the type of transforms used for standardised video coding schemes: often, a single transform is considered, usually a Discrete Cosine Transform (DCT). Recently, other transforms have started being considered in addition to the DCT. For instance, in the latest video coding standard, High Efficiency Video Coding (HEVC), the 4x4 sized blocks can make use of the Discrete Sine Transform (DST) and, in addition, it also possible not to transform them. This fact reveals an increasing interest to consider a plurality of transforms to achieve higher compression rates. This thesis focuses on extending HEVC through the use of multiple transforms. After a general introduction to video compression and transform coding, two transform designs are studied in detail: the Karhunen Loève Transform (KLT) and a Rate-Distortion Optimised Transform are considered. These two methods are compared against each other by replacing the transforms in HEVC. This experiment validates the appropriateness of the design. A coding scheme that incorporates and boosts the use of multiple transforms is introduced: several transforms are made available to the encoder, which chooses the one that provides the best rate-distortion trade-off. Consequently, a design method for building systems using multiple transforms is also described. With this coding scheme, significant amounts of bit-rate savings are achieved over HEVC, especially when using many complex transforms. However, these improvements come at the expense of increased complexity in terms of coding, decoding and storage requirements. As a result, simplifications are considered while limiting the impact on bit-rate savings. A first approach is introduced, in which incomplete transforms are used. This kind of transforms use one single base vector and are conceived to work as companions of the HEVC transforms. This technique is evaluated and provides significant complexity reductions over the previous system, although the bit-rate savings are modest. A systematic method, which specifically determines the best trade-offs between the number of transforms and bit-rate savings, is designed. This method uses two different types of transforms based separable orthogonal transforms and Discrete Trigonometric Transforms (DTTs) in particular. Several designs are presented, allowing for different complexity and bitrate savings trade-offs. These systems reveal the interest of using multiple transforms for video coding.

The FIRST program (Far Infrared Spectroscopy in the Troposphere) was created as an Instrument Incubator Program (IIP) by NASA Langley to demonstrate improved technology readiness levels (TRLs) for two technologies needed in the design of new imaging Fourier transform spectrometers (IFTS). The IIP IFTS was developed at the Space Dynamics Laboratory and flown to an altitude of 103,000 feet on an instrumented NASA balloon payload. The sensor collected approximately 15,000 interferograms during its 6-hour flight. Fourier transforms (FFT) produced acceptable results except for noise equivalent temperature differences (NETD) that were five times higher than goal and inconclusive transforms at seven strong absorption features. An alternate transform technique, maximum likelihood estimation (MLE), was implemented to improve spectral estimations at the absorptions and to improve the NETD for the sensor. Iterative expectation-maximization (EM) algorithms provide numerical solutions for the MLE. Four combinatorial forms of the EM algorithm were developed. Forms of the EM algorithm were developed to optimize amplitude estimations as a function of assumed noise distributions. 'Direct' and 'indirect' EM forms were developed to process the asymmetrical interferograms recorded by the FIRST sensor. The direct method extends the standard even (cosine) EM algorithm to simultaneously transform both the sine and cosine components of the interferogram. The indirect method, uses Fourier and inverse Fourier transforms as pre-processors to convert the measured asymmetrical interferograms to even (cosine) interferograms. Using the indirect Gaussian EM form improved the measured NETD by approximately twenty percent between 100 and 700 wavenumbers. For wavenumbers less than 100 or greater than 700, the improvement increased to a factor of at least two out to 1500 wavenumbers. The indirect Gaussian produced inconclusive results in the areas of high absorption because of large bias errors introduced by the FFT/IFFT pre-processing. The indirect method was found to be inadequate for estimating spectra at the deep absorptions. The direct EM method, on the other hand, has the potential to produce improved amplitude estimations at the absorptions since there are no inherent biases in the algorithm's initial conditions at a cost in computer resources and execution times that are four times those needed for the indirect method.

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