Pairs of Dual Wavelet Frames from
Any Two Refinable Functions |
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Authors: | Email author" target="_blank">Ingrid?DaubechieEmail author Email author" target="_blank">Bin?HanEmail author |
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Institution: | (1) Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA;(2) Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada |
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Abstract: | Starting from any two compactly supported refinable functions in L2(R)
with dilation factor d,we show that it is always possible to construct 2d wavelet functions
with compact support such that they generate a pair of dual d-wavelet frames in L2(R).
Moreover, the number of vanishing moments of each of these wavelet frames is equal
to the approximation order of the dual MRA; this is the highest possible. In particular,
when we consider symmetric refinable functions, the constructed dual wavelets are also
symmetric or antisymmetric. As a consequence, for any compactly supported refinable
function in L2(R), it is possible to construct, explicitly and easily, wavelets that are
finite linear combinations of translates (d · – k), and that generate a wavelet frame with
an arbitrarily preassigned number of vanishing moments.We illustrate the general theory
by examples of such pairs of dual wavelet frames derived from B-spline functions. |
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Keywords: | Dual wavelet frames Wavelet frames Refinable functions B-Spline functions |
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