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Kernel-Induced Sampling Theorem

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Title: Kernel-Induced Sampling Theorem
Authors: Tanaka, Akira Browse this author →KAKEN DB
Imai, Hideyuki Browse this author →KAKEN DB
Miyakoshi, Masaaki Browse this author
Keywords: Gramian matrix
Hilbert space
orthogonal projection
reproducing kernel
sampling theorem
Issue Date: Jul-2010
Publisher: IEEE - Institute of Electrical and Electronics Engineers
Journal Title: IEEE Transactions on Signal Processing
Volume: 58
Issue: 7
Start Page: 3569
End Page: 3577
Publisher DOI: 10.1109/TSP.2010.2046637
Abstract: A perfect reconstruction of functions in a reproducing kernel Hilbert space from a given set of sampling points is discussed. A necessary and sufficient condition for the corresponding reproducing kernel and the given set of sampling points to perfectly recover the functions is obtained in this paper. The key idea of our work is adopting the reproducing kernel Hilbert space corresponding to the Gramian matrix of the kernel and the given set of sampling points as the range space of a sampling operator and considering the orthogonal projector, defined via the range space, onto the closed linear subspace spanned by the kernel functions corresponding to the given sampling points. We also give an error analysis of a reconstructed function by incomplete sampling points.
Rights: © 2010 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Type: article
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 田中 章

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