TY - JOUR
T1 - Definability and stability of multiscale decompositions for manifold-valued data
AU - Grohs, Philipp
AU - Wallner, Johannes
N1 - 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.
PY - 2012/6
Y1 - 2012/6
N2 - 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.
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.
UR - http://hdl.handle.net/10754/597923
UR - https://linkinghub.elsevier.com/retrieve/pii/S001600321100041X
UR - http://www.scopus.com/inward/record.url?scp=84860307687&partnerID=8YFLogxK
U2 - 10.1016/j.jfranklin.2011.02.010
DO - 10.1016/j.jfranklin.2011.02.010
M3 - Article
SN - 0016-0032
VL - 349
SP - 1648
EP - 1664
JO - Journal of the Franklin Institute
JF - Journal of the Franklin Institute
IS - 5
ER -