Celebratio Mathematica — Daubechies

Complete Bibliography

Works connected to Bin Han

Filter the Bibliography List

year	title	people

			clear

I. Daubechies and B. Han: “The canonical dual frame of a wavelet frame,” Appl. Comput. Harmon. Anal. 12 : 3 (2002), pp. 269–285. MR 1912147 Zbl 1013.42023 article

I. Daubechies, B. Han, A. Ron, and Z. Shen: “Framelets: MRA-based constructions of wavelet frames,” Appl. Comput. Harmon. Anal. 14 : 1 (January 2003), pp. 1–46. MR 1971300 Zbl 1035.42031 article

Zuowei Shen	Related
Amos Ron	Related
Bin Han	Related

I. Daubechies and B. Han: “Pairs of dual wavelet frames from any two refinable functions,” Constr. Approx. 20 : 3 (2004), pp. 325–352. MR 2057532 Zbl 1055.42025 article

Starting from any two compactly supported refinable functions in \( L_2(\mathbf{R}) \) with dilation factor \( d \), we show that it is always possible to construct \( 2d \) wavelet functions with compact support such that they generate a pair of dual \( d \)-wavelet frames in \( L_2(\mathbf{R}) \). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function \( \phi \) in \( L_2(\mathbf{R}) \), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates \( \phi(d{\,\cdot\,} - k) \), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments. We illustrate the general theory by examples of such pairs of dual wavelet frames derived from \( B \)-spline functions.