On the stability of the PPH nonlinear multiresolution
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.
piecewise polynomial harmonic multiresolution
scientific article; zbMATH DE number 2164867