Projectable Multivariate Refinable Functions and Biorthogonal Wavelets

Abstract

A biorthogonal wavelet... In this paper, we introduce the concept of projectable refinable functions and demonstrate that many multivariate refinable functions are projectable; that is, they essentially carry the tensor product (separable) structure though themselves may be non-tensor product (nonseparable) refinable functions. For any pair of biorthogonal refinable functions (φ, φ^d) in L_2(R^n), when the refinable function φ is projectable, we prove that without loss of several desirable properties such as spatial localization, smoothness and approximation order, from the pair of biorthogonal refinable functions (φ, φ^d), we can easily obtain another pair of biorthogonal refinable functions in L_2(R^n) which are tensor product separable refinable functions. As an application, we show that there is no dual refinable function φ^d to the refinable basis function in the Loop scheme such that..