A novel method of constructing compactly supported orthogonal scaling functions from splines

A Construction of Bi orthogonal Functions to B splines with Multiple Knots

We present a construction of a re nable compactly supported vector of functions which is bi orthogonal to the vector of B splines of a given degree with multiple knots at the integers with prescribed multiplicity The construction is based on Hermite interpolatory subdivision schemes and on the relation between B splines and divided di erences The bi orthogonal vector of functions is shown to be...

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

Elliptic Scaling Functions as compactly Supported multivariate analogs of the B-splines

In the paper, we present a family of multivariate compactly supported scaling functions, which we call as elliptic scaling functions. The elliptic scaling functions are the convolution of elliptic splines, which correspond to homogeneous elliptic differential operators, with distributions. The elliptic scaling functions satisfy refinement relations with real isotropic dilation matrices. The ell...

Parameterization of Bivariate Nonseparable Orthogonal Symmetric Scaling Functions with Short Support

Let I be the 2 × 2 identity matrix, and M a 2 × 2 dilation matrix with M = 2I . First, we present the correlation of the scaling functions with dilation matrix M and 2I . Then by relating the properties of scaling functions with dilation matrix 2I to the properties of scaling functions with dilation matrix M , we give a parameterization of a class of bivariate nonseparable orthogonal symmetric ...

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