Definability and stability of multiscale decompositions for manifold-valued data
AbstractWe discuss multiscale representations of discrete manifold-valued data. As it turns out that we cannot expect general manifold analogs of biorthogonal wavelets to possess perfect reconstruction, we focus our attention on those constructions which are based on upscaling operators which are either interpolating or midpoint-interpolating. For definable multiscale decompositions we obtain a stability result. © 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
CitationGrohs P, Wallner J (2012) Definability and stability of multiscale decompositions for manifold-valued data. Journal of the Franklin Institute 349: 1648–1664. Available: http://dx.doi.org/10.1016/j.jfranklin.2011.02.010.
SponsorsThe authors gratefully acknowledge the support of the Austrian Science Fund. The work of Philipp Grohs has been supported by grant No. P19780. The research for this paper has been carried out while the author was working at the Center for Geometric Modeling and Scientific Visualization at KAUST, Saudi Arabia.