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Kernel-Induced Sampling Theorem

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タイトル: Kernel-Induced Sampling Theorem
著者: Tanaka, Akira 著作を一覧する
Imai, Hideyuki 著作を一覧する
Miyakoshi, Masaaki 著作を一覧する
キーワード: Gramian matrix
Hilbert space
orthogonal projection
reproducing kernel
sampling theorem
発行日: 2010年 7月
出版者: IEEE - Institute of Electrical and Electronics Engineers
誌名: IEEE Transactions on Signal Processing
巻: 58
号: 7
開始ページ: 3569
終了ページ: 3577
出版社 DOI: 10.1109/TSP.2010.2046637
抄録: 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.
資料タイプ: article
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 田中 章


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