Definability and stability of multiscale decompositions for manifold-valued data

Philipp Grohs; Johannes Wallner

doi:10.1016/j.jfranklin.2011.02.010

Definability and stability of multiscale decompositions for manifold-valued data

Philipp Grohs, Johannes Wallner

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	1648-1664
Number of pages	17
Journal	Journal of the Franklin Institute
Volume	349
Issue number	5
DOIs	https://doi.org/10.1016/j.jfranklin.2011.02.010
State	Published - Jun 2012
Externally published	Yes

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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10.1016/j.jfranklin.2011.02.010

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title = "Definability and stability of multiscale decompositions for manifold-valued data",

abstract = "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. {\textcopyright} 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.",

author = "Philipp Grohs and Johannes Wallner",

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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AU - Wallner, Johannes

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AB - 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.

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EP - 1664

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 5

ER -

Definability and stability of multiscale decompositions for manifold-valued data

Abstract

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