Smooth Multiwavelet Duals of Alpert Bases by Moment-Interpolating Refinement

Adaptive Solution of Partial DifferentialEquations in Multiwavelet Bases

Adaptive Solution of Partial Differential Equations in Multiwavelet Bases B. Alpert,∗,1 G. Beylkin,†,2 D. Gines,† and L. Vozovoi‡,3,4,5 ∗National Institute of Standards and Technology, Boulder, Colorado 80305-3328; †Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526; and ‡School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel E-mail: al...

Balanced multiwavelet bases based on symmetric FIR filters

This paper describes a basic difference between multiwavelets and scalar wavelets that explains, without using zero moment properties, why certain complications arise in the implementation of discrete multiwavelet transforms. Assuming we wish to avoid the use of prefilters in implementing the discrete multiwavelet transform, it is suggested that the behavior of the iterated filter bank associat...

Interpolating multiwavelet bases and the sampling theorem

This paper considers the classical sampling theorem in multiresolution spaces with scaling functions as interpolants. As discussed by Xia and Zhang, for an orthogonal scaling function to support such a sampling theorem, the scaling function must be cardinal (interpolating). They also showed that the only orthogonal scaling function that is both cardinal and of compact support is the Haar functi...

Dual multiwavelet frames with symmetry from two-direction renable functions

Multiwavelet bases with extra approximation properties

This paper highlights the differences between traditional wavelet and multiwavelet bases with equal approximation order. Because multiwavelet bases normally lack important properties that traditional wavelet bases (of equal approximation order) possess, the associated discrete multiwavelet transform is less useful for signal processing unless it is preceded by a preprocessing step (prefiltering...