Average sampling and reconstruction for reproducing kernel stochastic signals

This paper mainly considers the problem of reconstructing a reproducing kernel stochastic signal from its average samples. First, a uniform convergence result for reconstructing the deterministic reproducing kernel signals by an iterative algorithm is established. Then, we prove that the quadratic s...

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Published in:Mathematical methods in the applied sciences Vol. 39; no. 11; pp. 2930 - 2938
Main Authors: Jiang, Yingchun, Wang, Suping, Yang, Meixiang
Format: Journal Article
Language:English
Published: Freiburg Blackwell Publishing Ltd 01.07.2016
Wiley Subscription Services, Inc
Subjects:
Autocorrelation functions
average sampling
Convergence
Decay
Functions (mathematics)
Kernels
Mathematical analysis
mean square convergence
reproducing kernel space
Sampling
stochastic signals
Stochasticity
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:This paper mainly considers the problem of reconstructing a reproducing kernel stochastic signal from its average samples. First, a uniform convergence result for reconstructing the deterministic reproducing kernel signals by an iterative algorithm is established. Then, we prove that the quadratic sum of the corresponding reconstructed functions is uniformly bounded. Moreover, the reconstructed functions provide a frame expansion in the special case p = 2. Finally, the mean square convergence for recovering a weighted reproducing kernel stochastic signal from its average samples is given under some decay condition for the autocorrelation function, which can be removed for the case p = 2. Copyright © 2015 John Wiley & Sons, Ltd.
Bibliography:ark:/67375/WNG-NLJQJ21J-3
istex:CA354152F57B67818D2CA50D3257161A37AD2CCC
the Guangxi Key Laboratory of Cryptography and Information Security, Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Innovation Project of GUET Graduate Education - No. YJCXS201554
the Guangxi Natural Science Foundation - No. 2014GXNS FBA118012; No. 2013GXNSFAA019330
National Natural Science Foundation of China - No. 11201094
ArticleID:MMA3740
11161014
ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.3740