Time sampling and reconstruction in weighted reproducing kernel subspaces

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• 作者：Yingchun Jiang ^{guilinjiang@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Time encoding machine ; IF-sampling scheme ; Weighted reproducing kernel space ; Exact reconstruction ; Approximate reconstruction
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 December 2016
• 年：2016
• 卷：444
• 期：2
• 页码：1380-1402
• 全文大小：451 K

文摘

This paper mainly studies the time sampling and reconstruction of signals in weighted reproducing kernel subspaces of $L_{\nu }^p$. Firstly, a class of examples for weighted reproducing kernel subspaces are given. Then, using samples produced by a crossing time encoding machine or an Integrate-and-Fire time encoding machine satisfying some density constraints, iterative approximation algorithms are established for perfect recovery of signals in weighted reproducing kernel subspaces. Finally, an Integrate-and-Fire sampling scheme is discussed and an approximate reconstruction procedure is proposed for signals in weighted reproducing kernel subspaces. Moreover, we give detailed analysis for the approximate reconstruction method in the setting of shift-invariant subspaces.