Semi-regular Dubuc-Deslauriers wavelet tight frames

TL;DR

This paper develops wavelet tight frames with vanishing moments for semi-regular Dubuc-Deslauriers subdivision schemes, aiding regularity analysis of semi-regular subdivision processes.

Contribution

It introduces a novel construction of wavelet tight frames with vanishing moments for semi-regular Dubuc-Deslauriers schemes, using eigenvalue analysis and extension principles.

Findings

Constructed wavelet tight frames with n vanishing moments.

Provided approximation of the inverse Gramian for semi-regular schemes.

Enhanced tools for regularity analysis of semi-regular subdivision.

Abstract

In this paper, we construct wavelet tight frames with n vanishing moments for Dubuc-Deslauriers 2npoint semi-regular interpolatory subdivision schemes. Our motivation for this construction is its practical use for further regularity analysis of wide classes of semi-regular subdivision. Our constructive tools are local eigenvalue convergence analysis for semi-regular Dubuc-Deslauriers subdivision, the Unitary Extension Principle and the generalization of the Oblique Extension Principle to the irregular setting by Chui, He and St\"ockler. This group of authors derives suitable approximation of the inverse Gramian for irregular Bspline subdivision. Our main contribution is the derivation of the appropriate approximation of the inverse Gramian for the semi-regular Dubuc-Deslauriers scaling functions ensuring n vanishing moments of the corresponding framelets.