| 加权再生核空间中信号的平均采样与重构 |
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| 引用本文： | 蒋英春,王素萍. 加权再生核空间中信号的平均采样与重构[J]. 数学学报, 2016, 59(2): 233-246 |
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| 作者姓名： | 蒋英春 王素萍 |
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| 作者单位： | 桂林电子科技大学数学与计算科学学院 桂林 541004 |
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| 基金项目： | 国家自然科学基金资助项目(11201094,11161014);广西自然科学基金(2014GXNSFBA118012, 2013GXNSFAA019330),广西密码学与信息安全重点实验室及高校数据分析与计算重点实验室;桂林电子科技大学创新研究团队(微分方程与动力系统,计算机软件)项目及研究生教育创新计划资助项目(YJCXS201554) |
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| 摘 要： | 主要讨论L_v~p的加权再生核子空间中信号的平均采样与重构.首先,针对两种平均采样泛函建立了采样稳定性;其次,基于概率测度给出一个一般的迭代算法,将迭代逼近投影算法和迭代标架算法统一起来;最后,针对被白噪声污染的平均样本给出了信号重构的渐进点态误差估计.
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| 关 键 词： | 平均采样 加权再生核空间 迭代算法 点态误差估计 |
Reconstruction of Signals in Weighted Reproducing Kernel Spaces Based on Average Samples |
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| Ying Chun JIANG,Su Ping WANG. Reconstruction of Signals in Weighted Reproducing Kernel Spaces Based on Average Samples[J]. Acta Mathematica Sinica, 2016, 59(2): 233-246 |
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| Authors: | Ying Chun JIANG Su Ping WANG |
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| Affiliation: | School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China |
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| Abstract: | We mainly discuss the average sampling and reconstruction of signals in weighted reproducing kernel subspaces of Lνp . First, the sampling stability for two kinds of average sampling functionals are established. Then, we give a general iterative algorithm based on probability measure, which provides a unified treatment for iterative approximation projection algorithm and iterative frame algorithm. Finally, the asymptotic pointwise error estimate is presented for reconstructing a signal from its average samples corrupted by white noise. |
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| Keywords: | average sampling weighted reproducing kernel space iterative algorithm pointwise error estimate |
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