Definability and stability of multiscale decompositions for manifold-valued data

Philipp Grohs, Johannes Wallner

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


We 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.
Original languageEnglish (US)
Pages (from-to)1648-1664
Number of pages17
JournalJournal of the Franklin Institute
Issue number5
StatePublished - Jun 2012
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: The 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.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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