Construction of multivariate compactly supported tight wavelet frames |
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Authors: | Ming-Jun Lai,Joachim St ckler |
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Affiliation: | aDepartment of Mathematics, The University of Georgia, Athens, GA 30602,USA;bInstitut für Angewandte Mathematik, Universität Dortmund, D-44221 Dortmund, Germany |
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Abstract: | Two simple constructive methods are presented to compute compactly supported tight wavelet frames for any given refinable function whose mask satisfies the QMF or sub-QMF conditions in the multivariate setting. We use one of our constructive methods in order to find tight wavelet frames associated with multivariate box splines, e.g., bivariate box splines on a three or four directional mesh. Moreover, a construction of tight wavelet frames with maximum vanishing moments is given, based on rational masks for the generators. For compactly supported bi-frame pairs, another simple constructive method is presented. |
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Keywords: | Compactly supported wavelets Tight-frames Box splines Multi-resolution analysis Quadrature mirror filters |
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