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

Abstract EN

This paper is concerned with analyzing the mathematical properties, such as the regularity 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 same regularities as the ones based on the polynomial B-splines of the corresponding orders.

In the context of nonstationary wavelets, the stability of wavelet bases is not implied by the stability of a refinable function.

For this reason, we prove that the suggested nonstationary wavelets form Riesz bases for the space that they generate.