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Construction of Biorthogonal Wavelets Starting from Any Two Multiresolutions

A. Aldroubi, P. Abry, M. Unser

IEEE Transactions on Signal Processing, vol. 46, no. 4, pp. 1130-1133, April 1998.



Starting from any two given multiresolution analyses of L2, {V1j}j ∈ Z, and {V2j}j ∈ Z, we construct biorthogonal wavelet bases that are associated with this chosen pair of multiresolutions. Thus, our construction method takes a point of view opposite to the one of Cohen-Daubechies-Feauveau (CDF), which starts from a well-chosen pair of biorthogonal discrete filters. In our construction, the necessary and sufficient condition is the nonperpendicularity of the multiresolutions.


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AUTHOR="Aldroubi, A. and Abry, P. and Unser, M.",
TITLE="Construction of Biorthogonal Wavelets Starting from Any Two
        Multiresolutions",
JOURNAL="{IEEE} Transactions on Signal Processing",
YEAR="1998",
volume="46",
number="4",
pages="1130--1133",
month="April",
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