Analysis of Compactly Supported Nonstationary BiorthogonalWavelet Systems Based on Exponential B-Splines

摘要

This paper is concerned with analyzing the mathematical properties, such as theregularity and stability of nonstationary biorthogonal wavelet systems based on exponential B-splines. We first discuss the biorthogonality condition of the nonstationary refinable functions,and then we show that the refinable functions based on exponential B-splines have the sameregularities as the ones based on the polynomial B-splines of the corresponding orders. In thecontext of nonstationary wavelets, the stability of wavelet bases is not implied by the stability ofa refinable function. For this reason, we prove that the suggested nonstationary wavelets formRiesz bases for the space that they generate.