Convolution sampling and reconstruction of signals in a reproducing kernel subspace

Nashed, M.; Sun, Qiyu; Xian, Jun

doi:10.1090/S0002-9939-2012-11644-2

Convolution sampling and reconstruction of signals in a reproducing kernel subspace
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by M. Zuhair Nashed, Qiyu Sun and Jun Xian PDF

Proc. Amer. Math. Soc. 141 (2013), 1995-2007 Request permission

Abstract:

We consider convolution sampling and reconstruction of signals in certain reproducing kernel subspaces of $L^p, 1\le p\le \infty$. 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.

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