加权再生核空间中信号的平均采样与重构

蒋英春, 王素萍

数学学报 ›› 2016, Vol. 59 ›› Issue (2) : 233-246.

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数学学报 ›› 2016, Vol. 59 ›› Issue (2) : 233-246. DOI: 10.12386/A2016sxxb0021
论文

加权再生核空间中信号的平均采样与重构

    蒋英春, 王素萍
作者信息 +

Reconstruction of Signals in Weighted Reproducing Kernel Spaces Based on Average Samples

    Ying Chun JIANG, Su Ping WANG
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文章历史 +

摘要

主要讨论Lνp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.

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.

关键词

平均采样 / 加权再生核空间 / 迭代算法 / 点态误差估计

Key words

average sampling / weighted reproducing kernel space / iterative algorithm / pointwise error estimate

引用本文

导出引用
蒋英春, 王素萍. 加权再生核空间中信号的平均采样与重构. 数学学报, 2016, 59(2): 233-246 https://doi.org/10.12386/A2016sxxb0021
Ying Chun JIANG, Su Ping WANG. Reconstruction of Signals in Weighted Reproducing Kernel Spaces Based on Average Samples. Acta Mathematica Sinica, Chinese Series, 2016, 59(2): 233-246 https://doi.org/10.12386/A2016sxxb0021

参考文献

[1] Aldroubi A., Gröchenig K., Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Review, 2001, 43: 585-620.
[2] Aldroubi A., Sun Q., Tang W. S., Nonuniform average sampling and reconstruction in multiply generated shift-invariant spaces, Constr. Approx., 2004, 20: 173-189.
[3] Feichtinger H. G., Gewichtsfunktionen auf lokalkompakten Gruppen, Sitzber. d. Österr. Akad. Wiss., 1979, 188: 451-471.
[4] Feichtinger H. G., Gröchenig K., Iterative reconstruction of multivariate band-limited functions from irregular sampling values, SIAM J. Math. Anal., 1992, 231: 244-261.
[5] Gröchenig K., Reconstructing algorithms in irregular sampling, Math. Comput., 1992, 59: 181-194.
[6] Han D., Nashed M. Z., Sun Q., Sampling expansions in reproducing kernel Hilbert and Banach spaces, Numer. Funct. Anal. Optim., 2009, 30: 971-987.
[7] Van der Mee C., Nashed M. Z., Seatzu S., Sampling expansions and interpolation in unitarily translation invariant reproducing kernel Hilbert spaces, Adv. Comput. Math., 2003, 19: 355-372.
[8] Nashed M. Z., Sun Q., Sampling and reconstruction of signals in a reproducing kernel subspace of Lp(Rd), J. Funct. Anal., 2010, 258: 2422-2452.
[9] Nashed M. Z., Sun Q., TangW. S., Average sampling in L2, C. Acad. Sci. Paris, Ser I, 2009, 347: 1007-1010.
[10] Shannon C. E., Communication in the presence of noise, Proc. IRE, 1949, 37: 10-21.
[11] Sun Q., Non-uniform sampling and reconstruction for signals with finite rate of innovations, SIAM J. Math. Anal., 2006, 38: 1389-1422.
[12] Sun W., Zhou X., Average sampling in spline subspaces, Appl. Math. Lett., 2002, 15: 233-237.
[13] Sun W., Zhou X., Reconstruction of functions in spline subspaces from local averages, Proc. Amer. Math. Soc., 2003, 131: 2561-2571.
[14] Unser M., Sampling-50 years after Shannon, Proc. IEEE, 2000, 88: 569-587.
[15] Xian J., Weighted sampling and reconstruction in weighted reproducing kernel spaces, J. Math. Anal. Appl., 2010, 367: 34-42.

基金

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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