Name
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. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1109/TSP.2010.2046637 | IEEE Transactions on Signal Processing |
Keywords | Field | DocType |
gramian matrix,closed linear subspace,kernel-induced sampling theorem,corresponding reproducing kernel,sampling point,error analysis,kernel function,range space,reproducing kernel hilbert space,incomplete sampling point,sampling operator,nonuniform sampling,kernel,orthogonal projection,signal reconstruction,signal processing,hilbert space,history,sampling theorem,sampling methods,computer science education | Mathematical optimization,Mathematical analysis,Kernel embedding of distributions,Kernel principal component analysis,Bergman kernel,Representer theorem,Kernel method,Variable kernel density estimation,Mathematics,Reproducing kernel Hilbert space,Kernel (statistics) | Journal |
Volume | Issue | ISSN |
58 | 7 | 1053-587X |
Citations | PageRank | References |
1 | 0.38 | 6 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Akira Tanaka | 1 | 38 | 12.20 |
| Hideyuki Imai | 2 | 103 | 25.08 |
| Masaaki Miyakoshi | 3 | 99 | 20.27 |