Sampling and Galerkin reconstruction in reproducing kernel spaces

2014/10/07 by Cheng, Cheng, Jiang, Yingchun, Sun, Qiyu
#46E22 #65J22 #94A20 #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1410.1828

Abstract

In this paper, we consider sampling in a reproducing kernel subspace of L^p. 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.

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