We give a simple and explicit construction of primal and dual wavelet filters based on refinable multivariate splines (with respect to dilation matrices M) such that the corresponding wavelet functions generate dual affine frames of arbitrarily high regularity. Furthermore, the number of wavelets does not depend on the regularity. We apply the method also to generalized B-splines.
Salvatori, M., Soardi, P. (2002). Affine frames of multivariate box splines and their affine duals. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, 8(3), 269-290 [10.1007/s00041-002-0013-6].
Affine frames of multivariate box splines and their affine duals
SOARDI, PAOLO MAURIZIO
2002
Abstract
We give a simple and explicit construction of primal and dual wavelet filters based on refinable multivariate splines (with respect to dilation matrices M) such that the corresponding wavelet functions generate dual affine frames of arbitrarily high regularity. Furthermore, the number of wavelets does not depend on the regularity. We apply the method also to generalized B-splines.
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