Sampling and Galerkin reconstruction in reproducing kernel spaces

Cheng Cheng; Yingchun Jiang; Qiyu Sun

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arXiv · 1410.1828

Sampling and Galerkin reconstruction in reproducing kernel spaces

Cheng Cheng·Yingchun Jiang·Qiyu Sun

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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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BibTeX RIS

Cheng Cheng, Yingchun Jiang, Qiyu Sun. 2014-10-07. Sampling and Galerkin reconstruction in reproducing kernel spaces. https://arxiv.org/abs/1410.1828

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