Tight wavelet frames for subdivision

Authors:
Maria Charina;Joachim Stöckler
Affiliations:
Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany;Fachbereich Mathematik, Universität Dortmund, 44221 Dortmund, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

Citing 4
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Abstract

In this paper we construct multivariate tight wavelet frame decompositions for scalar and vector subdivision schemes with nonnegative masks. The constructed frame generators have one vanishing moment and are obtained by factorizing certain positive semi-definite matrices. The construction is local and allows us to obtain framelets even in the vicinity of irregular vertices. Constructing tight frames, instead of wavelet bases, we avoid extra computations of the dual masks. In addition, the frame decomposition algorithm is stable as the discrete frame transform is an isometry on @?"2, if the data are properly normalized.