A general framework of compactly supported splines and wavelets

Characterization of compactly supported refinable splines

We prove that a compactly supported spline function of degree k satisses the scaling equation (x) = P N n=0 c(n)(mx?n) for some integer m 2, if and only if (x) = P n p(n)B k (x?n) where p(n) are the coeecients of a polynomial P(z) such that the roots of P(z)(z ? 1) k+1 are mapped into themselves by the mapping z ! z m , and B k is the uniform B-spline of degree k. Furthermore, the shifts of for...

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

Biorthogonal Bases of Compactly Supported Wavelets

Orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide. We show here that under fairly general conditions, exact reconstruction schemes with synthesis filters different from the analysis filters give rise: to two dual Riesz bases of compactly supported wavelets. We give necessary ...

Construction of Compactly Supported Tight Wavelets Frames

Construction of Compactly Supported M-Band Wavelets

Let M ¢ 2 be a fixed positive integer. A family of closed subspaces Vj , j √ Z , of L 2 , the space of all square integrable functions on the real line, is said to be a multiresolution of L 2 if the following conditions hold: ( i) Vj , Vj/1 , and f √ Vj if and only if f ( Mr) √ Vj/1 for all j √ Z ; ( ii ) < j√Z Vj is dense in L 2 and > j√Z Vj Å M; ( iii ) there exists a function f in V0 such th...