2018/07/26 by Alberto Viscardi, Viscardi, Alberto
Computer Science · Engineering · #Advanced Numerical Analysis Techniques #Digital Filter Design and Implementation #FOS: Mathematics #Image and Signal Denoising Methods #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1807.10094
openalex publication_date 2018/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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 Stöckler. 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.