This dissertation develops a new wavelet design technique that produces a wavelet that matches a desired
signal in the least squares sense. The Wavelet Transform has become very popular in signal and image
processing over the last 6 years because it is a linear transform with an infinite number of possible basis
functions that provides localization in both time (space) and frequency (spatial frequency).
The Wavelet Transform is very similar to the matched filter problem, where the wavelet acts as a zero
mean matched filter. In pattern recognition applications where the output of the Wavelet Transform is
to be maximized, it is necessary to use wavelets that are specifically matched to the signal of interest.
Most current wavelet design techniques, however, do not design the wavelet directly, but rather, build a
composite wavelet from a library of previously designed wavelets, modify the bases in an existing multiresolution
analysis or design a multiresolution analysis that is generated by a scaling function which
has a specific corresponding wavelet. In this dissertation, an algorithm for finding both symmetric and
asymmetric matched wavelets is developed. It will be shown that under certain conditions, the matched
wavelets generate an orthonormal basis of the Hilbert space containing all finite energy signals. The
matched orthonormal wavelets give rise to a pair of Quadrature Mirror Filters (QMF) that can be used
in the fast Discrete Wavelet Transform. It will also be shown that as the conditions are relaxed...