Optimal matched wavelet construction and its application to image pattern recognition
Joseph O. Chapa, Raghuveer Rao · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1995
Wavelet transforms applied to multiresolution analyses of images produce outputs similar in theory to those of matched filters. In order to maximize the output at the location and scale of a signal of interest, it is necessary for the wavelet used in the multiresolution analysis to `match' the signal of interest. Current techniques match a signal to one of several predefined wavelets in a library, which requires wavelets to be designed in advance. Here, we present an alternative by developing a technique for deriving the wavelet directly from the desired signal spectrum in such a way that the mean squared error between their spectra is a minimum. Furthermore, the matched wavelet is designed such that its associated scaling function generates an orthonormal multiresolution analysis. The technique includes an algorithm for finding the scaling function from an orthonormal wavelet, and algorithms for finding the optimal wavelet magnitude and phase from a given input signal. Several examples are shown to demonstrate the performance of the technique for both known orthonormal wavelets and arbitrary signals.