On the Construction of Multivariate (Pre)Wavelets

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)

Construction of a class of trivariate nonseparable compactly supported wavelets with special dilation matrix

We present a method for  the construction of compactlysupported $left (begin{array}{lll}1 & 0 & -1\1 & 1 & 0 \1 &  0 & 1\end{array}right )$-wavelets  under a mild condition. Wavelets inherit thesymmetry of the corresponding scaling function and satisfies thevanishing moment condition originating in the symbols of the scalingfunction. As an application, an  example is  provided.

UNIVERSITY OF WISCONSIN-MADISON CENTER FOR THE MATHEMATICAL SCIENCES On the construction of multivariate (pre)wavelets

A new approach for the construction of wavelets and prewavelets on IR from multiresolution is presented. The method uses only properties of shift-invariant spaces and orthogonal projectors from L2(IR ) onto these spaces, and requires neither decay nor stability of the scaling function. Furthermore, this approach allows a simple derivation of previous, as well as new, constructions of wavelets, ...

Construction of compactly supported biorthogonal wavelets

This paper presents a construction of compactly supported biorthogonal spline wavelets in L2(IR ). In particular, a concrete method for the construction of bivariate compactly supported biorthogonal wavelets from box splines of increasing smoothness is provided. Several examples are given to illustrate the method. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines,...

Construction of compactly supported biorthogonal wavelets: I

This paper presents a construction of compactly supported dual functions of a given box spline in L2(IR ). In particular, a concrete method for the construction of compactly supported dual functions of bivariate box splines of increasing smoothness is provided. Key-Words:multivariate biorthogonal wavelets, multivariate wavelets, box splines, matrix extension