Level-Dependent Interpolatory Hermite Subdivision Schemes and Wavelets
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We study many properties of level-dependent Hermite subdivision, focusing on schemes preserving polynomial and exponential data. We specifically consider interpolatory schemes, which give rise to level-dependent multiresolution analyses through a prediction-correction approach. A result on the decay of the associated multiwavelet coefficients, corresponding to a uniformly continuous and differentiable function, is derived. It makes use of the approximation of any such function with a generalized Taylor formula expressed in terms of polynomials and exponentials.
KeywordsSubdivision schemes Hermite schemes Wavelets Coefficient decay
Mathematics Subject Classification65T60 65D15 41A58
This research was partially supported by the DFG Collaborative Research Center TRR 109, “Discretization in Geometry and Dynamics.” Most of this research was done while the second author was with the University of Passau. The second author also thanks the Department of Chemical and Biological Engineering, Princeton University, for their hospitality. The fourth author was partially supported by the Emmy Noether Research Group KR 4512/1-1.
- 14.Dyn, N., Levin, D.: Analysis of Hermite-type subdivision schemes. In: Chui, C.K., Schumaker, L.L. (eds.) Approximation Theory VIII. Vol 2: Wavelets and Multilevel Approximation, pp. 117–124. World Scientific, Singapore (1995)Google Scholar
- 20.Hoffmann, W., Papiernik, W., Sauer, T.: Method and device for guiding the movement of a moving machine element on a numerically controlled machine, Patent WO002006063945A1 (2006)Google Scholar
- 25.Uhlmann, V., Delgado-Gonzalo, R., Conti, C., Romani, L., Unser, M.: Exponential Hermite splines for the analysis of biomedical images. In: Proceedings of the 2014 IEEE International Conference on Acoustic, Speech and Signal Processing (ICASSP), pp. 1631–1634 (2014)Google Scholar