Compactly supported box-spline wavelets |
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Authors: | C K Chui J Stöckler J D Ward |
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Institution: | (1) Center for Approximation Theory Department of Mathematics, Texas A&M University, 77843-3368 College Station, TX;(2) Department of Mathematics, University of Duisburg, D-4100 Duisburg, Germany |
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Abstract: | A general procedure for constructing multivariate non-tensor-product wavelets that generate an orthogonal decomposition ofL
2(R)s,s s≥1, is described and applied to yield explicit formulas for compactly supported spline-wavelets based on the multiresolution
analysis ofL
2(R)s 1≤s≤3, generated by any box spline whose direction set constitutes a unimodular matrix. In particular, when univariate cardinal
B-splines are considered, the minimally supported cardinal spline-wavelets of Chui and Wang are recovered. A refined computational
scheme for the orthogonalization of spaces with compactly supported wavelets is given. A recursive approximation scheme for
“truncated” decomposition sequences is developed and a sharp error bound is included. A condition on the symmetry or anti-symmetry
of the wavelets is applied to yield symmetric box-spline wavelets.
Partially supported by ARO Grant DAAL 03-90-G-0091
Partially supported by NSF Grant DMS 89-0-01345
Partially supported by NATO Grant CRG 900158. |
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