M-Band Burt–Adelson Biorthogonal Wavelets |
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Authors: | Mauro Maggioni |
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Institution: | Department of Mathematics, Washington University, Campus Box 1146, St. Louis, Missouri, 63130, f1, www.math.wustl.edu/ maggioni |
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Abstract: | For every integer M>2 we introduce a new family of biorthogonal MRAs with dilation factor M, generated by symmetric scaling functions with small support. This construction generalizes Burt–Adelson biorthogonal 2-band wavelets. For M{3,4} we are able to find simple explicit expressions for two different families of wavelets associated with these MRAs: one with better localization and the other with interesting symmetry–antisymmetry properties. We study the regularity of our scaling functions by determining their Sobolev exponent, for every value of the parameter and every M. We also study the critical exponent when M=3. |
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Keywords: | M-band wavelets M-band symmetric scaling functions biorthogonal systems multiresolution analysis Sobolev exponent |
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