Spline interpolation and wavelet construction
type: Item
instance of: scholarly article
title: Spline interpolation and wavelet construction
zbMATH Open document ID: 0914.42024
author: K. Appert
published in: Applied and Computational Harmonic Analysis
publication date: 1999-06-02T00:00:00Z
review text: The method of Dubuc and Deslauriers on symmetric interpolatory subdivision is extended to study the relationship between interpolation processes and wavelet construction. Refinable and interpolatory functions are constructed in stages from \(B\)-splines. Their method constructs the filter sequence (its Laurent polynomial) of the interpolatory function as a product of Laurent polynomials. This provides a natural way of splitting the filter for the construction of orthonormal and biorthogonal scaling functions leading to orthonormal and biorthogonal wavelets. Their method also leads to a class of filters which includes the minimal length Daubechies compactly supported orthonormal wavelet coefficients. Examples of ``good'' filters are given, together with results of numerical experiments conducted to test the performance of these filters in data compression.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 41A15
zbMATH DE Number: 1221109
zbMATH Keywords: refinable function
zbMATH Keywords: wavelets
zbMATH Keywords: interpolatory function
zbMATH Keywords: uniform B-spline
zbMATH Keywords: Euler-Frobenius polynomial
zbMATH Keywords: Riesz basis
zbMATH Keywords: biorthogonal basis
zbMATH Keywords: transition operator
zbMATH Keywords: subdivision algorithm
zbMATH Keywords: cascade algorithm
reviewed by: Richard A. Zalik
MaRDI profile type: Publication
OpenAlex ID: W2088974070
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DOI: 10.1006/ACHA.1997.0232
description: scientific article; zbMATH DE number 1221109