Convolution sampling and reconstruction of signals in a reproducing kernel subspace

Abstract

We consider convolution sampling and reconstruction of signals in certain reproducing kernel subspaces of L p , 1 ≤ p ≤ ∞ L^p, 1\le p\le \infty . We show that signals in those subspaces could be stably reconstructed from their convolution samples taken on a relatively separated set with small gap. Exponential convergence and error estimates are established for the iterative approximation-projection reconstruction algorithm.