On the stability of the PPH nonlinear multiresolution
type: Item
instance of: scholarly article
title: On the stability of the PPH nonlinear multiresolution
zbMATH Open document ID: 1077.65138
author: Sergio Amat
author: J. Liandrat
published in: Applied and Computational Harmonic Analysis
publication date: 2005-05-04T00:00:00Z
review text: The authors study the stability properties of the piecewise polynomial harmonic (PPH) multiresolution transform, introduced recently by the authors, \textit{R. Donat} and \textit{J. C. Trillo} [Analysis of a fully nonlinear multiresolution scheme for image processing, Preprint U. P. Cartagena 38 (2004)]. In this paper, the PPH multiresolution is presented as a nonlinear perturbation of a linear subdivision scheme (centered Lagrange interpolation of degree 1 or 3). As a result, special difference operators between discretization levels, are proved to be contractions. This, in turn, leads to the convergence and stability results for PPH multiresolution.
reviewed by: Wojciech Czaja
Mathematics Subject Classification ID: 65T60
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D18
Mathematics Subject Classification ID: 94A08
zbMATH DE Number: 2164867
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: nonlinear multiresolution
zbMATH Keywords: piecewise polynomial harmonic multiresolution
zbMATH Keywords: subdivision schemes
zbMATH Keywords: image processing
zbMATH Keywords: centered Lagrange interpolation
MaRDI profile type: Publication
full work available at URL: j.acha.2004.12.002
OpenAlex ID: W2052329331
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DOI: 10.1016/J.ACHA.2004.12.002
description: scientific article; zbMATH DE number 2164867