A construction of interpolating wavelets on invariant sets |
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Authors: | Zhongying Chen Charles A. Micchelli Yuesheng Xu. |
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Affiliation: | Department of Scientific Computation, Zhongshan University, Guangzhou 510275, P. R. China ; IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598-0218 ; Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105 |
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Abstract: | We introduce the concept of a refinable set relative to a family of contractive mappings on a metric space, and demonstrate how such sets are useful to recursively construct interpolants which have a multiscale structure. The notion of a refinable set parallels that of a refinable function, which is the basis of wavelet construction. The interpolation points we recursively generate from a refinable set by a set-theoretic multiresolution are analogous to multiresolution for functions used in wavelet construction. We then use this recursive structure for the points to construct multiscale interpolants. Several concrete examples of refinable sets which can be used for generating interpolatory wavelets are included. |
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Keywords: | Refinable sets set wavelets interpolating wavelets |
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