Optimal Learning Of Bandlimited Functions From Localized Sampling

Charles A. Micchelli; Yuesheng Xu; Haizhang Zhang

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Optimal Learning Of Bandlimited Functions From Localized Sampling

机译：从局部采样中学习带限函数

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摘要

An optimal algorithm for approximating bandlimited functions from localized sampling is established. Several equivalent formulations for the approximation error of the optimal algorithm are presented and its upper and lower bound estimates for the univariate case are provided. The estimates show that the approximation error decays exponentially (but not faster) as the number of localized samplings increases. As a consequence of these results, we obtain an upper bound estimate for the eigenvalues of an integral operator that arises in the bandwidth problem.

机译：建立了一种从局部采样近似带限函数的最优算法。给出了最佳算法逼近误差的几种等效公式，并提供了单变量情况下的上下界估计。估计表明，随着局部采样数量的增加，近似误差呈指数衰减（但不会更快）。这些结果的结果是，我们获得了带宽问题中出现的积分算子特征值的上限估计。

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来源
《Journal of complexity》 |2009年第2期|85-114|共30页
作者
Charles A. Micchelli; Yuesheng Xu; Haizhang Zhang;
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作者单位

Department of Mathematics and Statistics, State University of New York. The University at Albany. Albany, NY 12222, USA;

Department of Mathematics, Syracuse University, Syracuse, NY 13244, USA;

Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;

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正文语种 eng
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关键词
whittaker-shannon series; bandlimited signals; optimal algorithms; error estimates; translation invariant kernels; the bandwidth problem;

机译：惠特克-香农级数;带限信号;最优算法;误差估计;平移不变核;带宽问题;

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1. Generalised filters and optimum sampling frequencies for the reconstruction of bandlimited signals from past samples [J] . Le Bihan J., Watkins L.R. Electronics Letters . 1993,第24期

机译：通用滤波器和最佳采样频率，可从过去的采样中重建带限信号
2. An extension to the sampling theorem for lowpass bandlimited periodic time functions using Nth-order sampling schemes [J] . Summers B., Cain G.D. IEEE Transactions on Instrumentation and Measurement . 1991,第6期

机译：使用N阶采样方案对低通带限周期时间函数的采样定理的扩展
3. Nonuniform Sampling and Recovery of Multidimensional Bandlimited Functions by Gaussian Radial-Basis Functions [J] . Journal of Fourier Analysis and Applications . 2011,第3期

机译：高斯径向基函数对多维带限函数的非均匀采样和恢复
4. On Send-on-Delta Sampling of Bandlimited Functions [C] . Adrian E. G. Huber, Shih-Chii Liu International Conference on Sampling Theory and Applications . 2017

机译：关于带状函数的发送Δ采样
5. Increased signalling efficiency is mediated by optimal co-localization of TCR and CD8 within lipid rafts: A novel mechanism for the control of functional avidity. [D] . Cawthon, Andrew Grover. 2002

机译：脂质筏中TCR和CD8的最佳共定位可提高信号传导效率：一种控制功能亲和力的新机制。
6. Learning Task-Optimal Registration Cost Functions for Localizing Cytoarchitecture and Function in the Cerebral Cortex [O] . B. T. Thomas Yeo, Mert R. Sabuncu, Tom Vercauteren, -1

机译：学习本地化细胞构筑任务优化注册成本函数和函数在大脑皮层
7. Optimal learning of bandlimited functions from localized sampling [O] . Micchelli Charles A., Xu Yuesheng, Zhang Haizhang 2009

机译：通过局部采样优化学习带限函数

Optimal Learning Of Bandlimited Functions From Localized Sampling

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