Data compression on the sphere using multiscale radial basis function approximation

We propose two new approaches for efficiently compressing unstructured data defined on the unit sphere. Both approaches are based upon a meshfree multiscale representation of functions on the unit sphere. This multiscale representation employs compactly supported radial basis functions of different...

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Bibliographic Details
Published in:Advances in computational mathematics 2014-08, Vol.40 (4), p.923-943
Main Authors: Le Gia, Q. T., Wendland, H.
Format: Article
Language:English
Subjects:
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
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Summary:We propose two new approaches for efficiently compressing unstructured data defined on the unit sphere. Both approaches are based upon a meshfree multiscale representation of functions on the unit sphere. This multiscale representation employs compactly supported radial basis functions of different scales. The first approach is based on a simple thresholding strategy after the multiscale representation is computed. The second approach employs a dynamical discarding strategy, where small coefficients are already discarded during the computation of the approximate multiscale representation. We analyse the (additional) error which comes with either compression and provide numerical experiments using topographical data of the earth.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-013-9334-z