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   -> Volume 4, Issue 5

Preprint: Optimal Matched Wavelet Construction...
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Author Message (Joe Chapa)

PostPosted: Tue Dec 03, 2002 11:34 am    
Subject: Preprint: Optimal Matched Wavelet Construction...
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Preprint: Optimal Matched Wavelet Construction...

Title: Optimal Matched Wavelet Construction and Its
Application to Image Pattern Recognition

Authors: Joseph O. Chapa, Maj, USAF
Center for Imaging Science
Rochester Institute of Technology
Rochester, NY

Mysore R. Raghuveer
Dept. of Electrical Engineering
Rochester Institute of Technology
Rochester, NY

Presented At: Conference on Wavelet Applications for Dual Use
SPIE's 1995 Symposium on OE/Aerospace Sensing
and Dual Use Photonics

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Wavelet transforms applied to multiresolution analyses of
images produce outputs similar in theory to those of matched
filters. In order to maximize the outputat 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 a bandlimited 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. Two
examples are shown to demonstrate the performance of the
technique for both known orthonormal wavelets and arbitrary signals.
Keywords: wavelet construction, bandlimited wavelets,
matched wavelet, pattern recognition.
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