Sampling and Galerkin reconstruction in reproducing kernel spaces

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• 作者：Cheng Cheng^a ; ^{cheng.cheng@knights.ucf.edu" class="auth_mail" title="E-mail the corresponding author} ; Yingchun Jiang^b ; ^{guilinjiang@126.com" class="auth_mail" title="E-mail the corresponding author} ; Qiyu Sun^a ; ^{qiyu.sun@ucf.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：94A20 ; 46E22 ; 65J22
• 刊名：Applied and Computational Harmonic Analysis
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：41
• 期：2
• 页码：638-659
• 全文大小：1703 K

文摘

In this paper, we introduce a fidelity measure depending on a given sampling scheme and we propose a Galerkin method in Banach space setting for signal reconstruction. 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 in a reproducing kernel subspace of L^p$L^p$. Also we present detailed analysis and numerical simulations of the Galerkin method for reconstructing signals with finite rate of innovation.