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

Thesis (Ph. D.)--Florida State University, 2006. / Advisor: Simon Foo, Florida State University, FAMU-FSU College of Engineering, Dept. of Electrical and Computer Engineering. Title and description from dissertation home page (viewed June 15, 2006). Document formatted into pages; contains xii, 131 pages. Includes bibliographical references.

Thesis (Ph. D.)--Industrial and Systems Engineering, Georgia Institute of Technology, 2006. / Huo, Xiaoming, Committee Member ; Heil, Chris, Committee Member ; Wang, Yang, Committee Member ; Hayter, Anthony, Committee Member ; Vidakovic, Brani, Committee Chair.

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This thesis uses the powerful mathematics of wavelet packet signal processing to efficiently extract features from sampled acoustic spectra for the purpose of discriminating between different classes of sounds. An algorithm called dictionary projection pursuit (DPP) is developed which is a fast approximate version of the projection pursuit (PP) algorithm [P.J. Huber Projection Pursuit, Annals of Statistics, 13 ( 2) 435–525, 1985]. When used with a wavelet packet or cosine packet dictionary, this algorithm is significantly faster than the PP algorithm with relatively little degradation in performance provided that the multivariate vectors are samples of an underlying continuous waveform or image. The DPP algorithm is applied to the problem of approximating the Karhunen-Loève transform (KLT) in high dimensional spaces and simulations are performed to compare this algorithm to Wickerhauser's approximate KLT algorithm [M.V. Wickerhauser. Adapted Wavelet Analysis from Theory to Software, A.K. Peters Ltd, 1994]. Both algorithms perform very well relative to the eigenanalysis form of the KLT algorithm at a small fraction of the computational cost. The DPP algorithm is then applied to the problem of finding discriminant features in acoustic spectra for sound recognition tasks; extensive simulations are performed to compare this algorithm to previously developed dictionary methods for discrimination such as Saito and Coifman's local discriminant bases [N. Saito and R. Coifman. Local Discriminant Bases and their Applications. Journal of Mathematical Imaging and Vision, 5 (4) 337–358, 1995] and Buckheit and Donoho's discriminant pursuit [J. Buckheit and D. Donoho. Improved Linear Discrimination Using Time-Frequency Dictionaries. Proceedings of SPIE Wavelet Applications in Signal and Image Processing III Vol 2569, 540–551, July, 1995]. It is found that each feature extraction algorithm performs well under different conditions, but the DPP algorithm is the most flexible and consistent performer. / Graduate

In this paper I formulate an explicit wavelet transform that, applied to any distribution in S^1(R^2), yields a function on phase space whose high-frequency singularities coincide precisely with the wave front set of the distribution. This characterizes the wave front set of a distribution in terms of the singularities of its wavelet transform with respect to a suitably chosen basic wavelet.

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The task of determining the types of objects present in the scene, or object recognition is one of the fundamental problems of computer vision. Applications include, medical imaging, security, and multi-media database search. For example, before attempting to detect suspicious behavior, an automated surveillance system would have to determine the classes of objects that are attempting to interact. This task is adversely affected by poor quality video or images. For my thesis I addressed the problem of differentiating between pedestrians and vehicles in both Infra Red and Electro Optical videos. The problem was made quite difficult by the targets: small size, poor quality of the video as well as the precision of the moving target indicator algorithm. However combining the inverse wavelet transform (IDWI) for feature extraction and the Support Vector Machine (SVM) for actual classification provided results superior to other features, and machine learning techniques.

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.