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• W2044305453 abstract "In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of $L^p(Rd), 1le ple infty$, associated with an idempotent integral operator whose kernel has certain off-diagonal decay and regularity. The space of $p$-integrable non-uniform splines and the shift-invariant spaces generated by finitely many localized functions are our model examples of such reproducing kernel subspaces of $L^p(Rd)$. We show that a signal in such reproducing kernel subspaces can be reconstructed in a stable way from its samples taken on a relatively-separated set with sufficiently small gap. We also study the exponential convergence, consistency, and the asymptotic pointwise error estimate of the iterative approximation-projection algorithm and the iterative frame algorithm for reconstructing a signal in those reproducing kernel spaces from its samples with sufficiently small gap." @default.
• W2044305453 created "2016-06-24" @default.
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• W2044305453 date "2010-04-01" @default.
• W2044305453 modified "2023-10-01" @default.
• W2044305453 title "Sampling and reconstruction of signals in a reproducing kernel subspace of <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si1.gif overflow=scroll><mml:msup><mml:mi>L</mml:mi><mml:mi>p</mml:mi></mml:msup><mml:mo stretchy=false>(</mml:mo><mml:msup><mml:mi mathvariant=double-struck>R</mml:mi><mml:mi>d</mml:mi></mml:msup><mml:mo stretchy=false>)</mml:mo></mml:math>" @default.
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• W2044305453 doi "https://doi.org/10.1016/j.jfa.2009.12.012" @default.
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