SAMPLING AND RECONSTRUCTION OF SIGNALS IN A REPRODUCING KERNEL SUBSPACE OF Lp(Rd)
نویسندگان
چکیده
In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of L(R), 1 ≤ p ≤ ∞, 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(R). 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.
منابع مشابه
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