Wavelets and framelets from dual pseudo splines

TL;DR

This paper introduces a new class of refinable functions called dual pseudo splines, and constructs associated Riesz wavelets and tight frame systems with specific approximation properties.

Contribution

It develops the theory of dual pseudo splines and demonstrates their use in constructing wavelets and frames with desirable mathematical properties.

Findings

Constructed Riesz wavelets from dual pseudo splines.

Developed tight frame systems with specified approximation order.

Extended the application of dual pseudo splines in wavelet theory.

Abstract

Dual pseudo splines constitute a new class of refinable functions with B-splines as special examples, which was introduced in \cite{DHSS}. In this paper, we shall construct Riesz wavelet associated with dual pseudo splines. Furthermore, we use dual pseudo splines to construct tight frame systems with desired approximation order by applying the unitary extension principle.