| 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. |
