In this dissertation, a new cubic-spline interpolation (CSI) for both one-dimensional and two-dimensional signals is developed to sub-sample signal, image and video compression data. This new interpolation scheme that is based on the least-squares method with a cubic-spline function can be implemented by the fast Fourier transform (FFT). The result is a simpler and faster interpolation scheme than can be obtained by other conventional means. It is shown by computer simulation that such a new CSI yields a very accurate algorithm for smoothing. Linear interpolation, linear-spline interpolation, cubic-convolution interpolation and cubic B-spline interpolation tend to be inferior in performance. In addition it is shown in this dissertation that the CSI scheme can be performed by a fast and efficient computation. The proposed method uses a simpler technique in the decimation process. It requires substantially fewer additions and multiplications than the original CSI algorithm. Moreover, a new type of overlap-save scheme is utilized to solve the boundary-condition problems that occur between two neighboring subimages in the actual image. It is also shown in this dissertation that a very efficient 9-point Winograd discrete Fourier transform (Winograd DFT) can be used to replace the FFT needed to implement the CSI scheme. Furthermore, the proposed fast new CSI scheme is used along with the Joint Photographic Experts Group (JPEG) standard to design a modified JPEG encoder- decoder for image data compression. As a consequence, for higher compression ratios the proposed modified JPEG encoder-decoder obtains a better quality of reconstructed image and also requires less computational time than both the conventional JPEG method and the America on Line (AOL) algorithm. Finally, the new fast CSI scheme is applied to the JPEG 2000, MPEG-1 and MPEG-2 algorithms, respectively. A computer simulation shows that in the encoding and decoding, the proposed modified JPEG 2000 encoder-decoder speeds up the JPEG 2000 standard, respectively, and still obtains a good quality of reconstructed image that is similar to JPEG 2000 standard for high compression ratios. Additionally, the reconstructed video using the modified MPEG encoder-decoder indicates a better quality than the conventional MPEG-1 and MPEG-2 algorithms for high compression ratios or low-bit rates.

Zugl.: Siegen, Univ., Diss., 2009

Zugl.: Kaiserslautern, Techn. Univ., Diss., 2009

Zugl.: Erlangen, Nürnberg, Univ., Diss., 2008

<p>The numerical path integration method for solving stochastic differential equations is extended to solve systems up to six spatial dimensions, angular variables, and highly nonlinear systems - including systems that results in discontinuities in the response probability density function of the system. Novel methods to stabilize the numerical method and increase computation speed are presented and discussed. This includes the use of the fast Fourier transform (FFT) and some new spline interpolation methods. Some sufficient criteria for the path integration theory to be applicable is also presented. The development of complex numerical code is made possible through automatic code generation by scripting. The resulting code is applied to chaotic dynamical systems by adding a Gaussian noise term to the deterministic equation. Various methods and approximations to compute the largest Lyapunov exponent of these systems are presented and illustrated, and the results are compared. Finally, it is shown that the location and size of the additive noise term affects the results, and it is shown that additive noise for specific systems could make a non-chaotic system chaotic, and a chaotic system non-chaotic.</p>

Two extensions to the proper orthogonal decomposition (POD) technique are considered for steady transonic aerodynamic applications. The first is to couple the POD approach with a cubic spline interpolation procedure in order to develop fast, low-order models that accurately capture the variation in parameters, such as the angle of attack or inflow Mach number. The second extension is a POD technique for the reconstruction of incomplete or inaccurate aerodynamic data. First, missing flow field data is constructed with an existing POD basis constructed from complete aerodynamic data. Second, a technique is used to develop a complete snapshots from an incomplete set of aerodynamic snapshots. / Singapore-MIT Alliance (SMA)

The numerical path integration method for solving stochastic differential equations is extended to solve systems up to six spatial dimensions, angular variables, and highly nonlinear systems - including systems that results in discontinuities in the response probability density function of the system. Novel methods to stabilize the numerical method and increase computation speed are presented and discussed. This includes the use of the fast Fourier transform (FFT) and some new spline interpolation methods. Some sufficient criteria for the path integration theory to be applicable is also presented. The development of complex numerical code is made possible through automatic code generation by scripting. The resulting code is applied to chaotic dynamical systems by adding a Gaussian noise term to the deterministic equation. Various methods and approximations to compute the largest Lyapunov exponent of these systems are presented and illustrated, and the results are compared. Finally, it is shown that the location and size of the additive noise term affects the results, and it is shown that additive noise for specific systems could make a non-chaotic system chaotic, and a chaotic system non-chaotic.

This thesis applies the one-dimensional (1-D) and two-dimensional (2-D) cubic-spline interpolation (CSI) schemes to MPEG standard for very low-bit rate video coding. In addition, the CSI scheme is used to implement the scalable video compression scheme in this thesis. The CSI scheme is based on the least-squares method with a cubic convolution function. It has been shown that the CSI scheme yields a very accurate algorithm for smoothing and obtains a better quality of reconstructed image than linear interpolation, linear-spline interpolation, cubic convolution interpolation, and cubic B-spline interpolation. In order to obtain a very low-bit rate video, the CSI scheme is used along with the MPEG-1 standard for video coding. Computer simulations show that this modified MPEG not only avoids the blocking effect caused by MPEG at high compression ratio but also gets a very low-bit rate video coding scheme that still maintains a reasonable video quality. Finally, the CSI scheme is also used to achieve the scalable video compression. This new scalable video compression scheme allows the data rate to be dynamically changed by the CSI scheme, which is very useful when operates under communication networks with different transmission capacities.

Zugl.: Kaiserslautern, Techn. Univ., Diss., 2007

This thesis covers a utility optimizing model designed and calibrated for agents of the Swedish economy. The main ingredient providing for this specific country is the modeling of the pension accumulation and pension benefits, which closely mimics the Swedish system. This characteristic is important since it measures one of the only two diversities between genders, that is, the income. The second characteristic is the survival probability. Except for these differences in national statistics, men and women are equal. The reminding model parameters are realistically set estimates from the surrounding economy. When using the model, firstly a baseline agent representing the entire labor force is under the microscope for evaluating the model itself. Next, one representative woman and one representative man from the private and public sectors respectively, composes a set of four samples for investigation of heterogeneity in optimality. The optimum level of consumption and risk-proportion of liquid wealth are solved by maximizing an Epstein-Zin utility function using the method of dynamic programming. The results suggests that both genders benefit from adapting the customized solutions to the problem.