Sampling and Galerkin reconstruction in reproducing kernel spaces
Information Theory
2014-10-08 v1 math.IT
Numerical Analysis
Abstract
In this paper, we consider sampling in a reproducing kernel subspace of . We introduce a pre-reconstruction operator associated with a sampling scheme and propose a Galerkin reconstruction in general Banach space setting. We show that the proposed Galerkin method provides a quasi-optimal approximation, and the corresponding Galerkin equations could be solved by an iterative approximation-projection algorithm. We also present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.
Cite
@article{arxiv.1410.1828,
title = {Sampling and Galerkin reconstruction in reproducing kernel spaces},
author = {Cheng Cheng and Yingchun Jiang and Qiyu Sun},
journal= {arXiv preprint arXiv:1410.1828},
year = {2014}
}