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Author
Date
2012-01Type
- Report
ETH Bibliography
yes
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Abstract
The present paper is concerned with the study of manifold-valued multiscale transforms with a focus on the Stiefel manifold. For this speci c geometry we derive several formulas and algorithms for the computation of geometric means which will later enable us to construct multiscale transforms of wavelet type. As an application we study compression of piecewise smooth families of low-rank matrices both for synthetic data and also real-world data arising in hyperspectral imaging. As a main theoretical contribution we show that the manifold-valued wavelet transforms can achieve an optimal N-term approximation rate for piecewise smooth functions with possible discontinuities. This latter result is valid for arbitrary manifolds. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010396279Publication status
publishedExternal links
Journal / series
SAM Research ReportVolume
Publisher
Seminar for Applied Mathematics, ETH ZurichSubject
Riemannian data; low-rank approximation; N-term approximation; compression; manifold-valued wavelet transformsOrganisational unit
03435 - Schwab, Christoph / Schwab, Christoph
Funding
247277 - Automated Urban Parking and Driving (EC)
Notes
Journal: Computer Aided Geometric Design, 2012.More
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ETH Bibliography
yes
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