Digital Total Variation Filtering as Postprocessing for Radial Basis Function Approximation Methods

Digital total variation (DTV) filtering techniques, that originated in the field of image processing, are adapted to postprocess radial basis function approximations of piecewise continuous functions. Through numerical examples, we show that DTV filtering is a fast, robust, postprocessing method tha...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2006-09, Vol.52 (6), p.1119-1130
Main Author: Sarra, S.A.
Format: Article
Language:English
Subjects:
Approximation
Digital
Digital total variation filtering
Discontinuity
Filtering
Filtration
Gibbs phenomena
Mathematical analysis
Mathematical models
Meshfree
Postprocessing
Radial basis function
Radial basis functions
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Summary:Digital total variation (DTV) filtering techniques, that originated in the field of image processing, are adapted to postprocess radial basis function approximations of piecewise continuous functions. Through numerical examples, we show that DTV filtering is a fast, robust, postprocessing method that can be used to remove Gibbs oscillations while sharply resolving discontinuities. The method is applicable for arbitrarily located data points. A postprocessing method for scattered data had not been given previously.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2006.02.013