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Construction of multivariate compactly supported tight wavelet frames. (English) Zbl 1106.42028
Summary: 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.
MSC:
42C40Wavelets and other special systems
42C30Completeness of sets of functions of non-trigonometric Fourier analysis