Sampling and reconstruction of signals in a reproducing kernel subspace of L-P(R-d)
Abbreviated Journal Title
J. Funct. Anal.
Sampling; Iterative reconstruction algorithm; Reproducing kernel spaces; Idempotent operators; p-Frames; SHIFT-INVARIANT SPACES; INTEGRABLE GROUP-REPRESENTATIONS; FINITE RATE; ATOMIC DECOMPOSITIONS; HILBERT-SPACES; NOISY SAMPLES; ITERATIVE; RECONSTRUCTION; L-P; INNOVATION; SHANNON; Mathematics
In this paper, we consider sampling and reconstruction of signals in a reproducing kernel subspace of L-p(R-d), 1 <= p <= infinity, 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(R-d). 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. (C) 2009 Elsevier Inc. All rights reserved.
Journal of Functional Analysis
"Sampling and reconstruction of signals in a reproducing kernel subspace of L-P(R-d)" (2010). Faculty Bibliography 2010s. 581.