Average sampling and reconstruction for reproducing kernel stochastic signals

2015 ◽  
Vol 39 (11) ◽  
pp. 2930-2938
Author(s):  
Yingchun Jiang ◽  
Suping Wang ◽  
Meixiang Yang
Keyword(s):  
Reproducing Kernel ◽  
Stochastic Signals ◽  
Average Sampling ◽  
Sampling And Reconstruction

scholarly journals Average sampling in mixed shift-invariant subspaces with generators in hybrid-norm spaces

2021 ◽  
Author(s):  
Haizhen Li ◽  
Yan Tang
Keyword(s):  
Exponential Convergence ◽  
Invariant Subspaces ◽  
Time Varying ◽  
Projection Algorithms ◽  
Iterative Approximation ◽  
Wiener Amalgam Space ◽  
Average Sampling ◽  
Norm Space ◽  
Sampling And Reconstruction ◽  
Mixed Lebesgue Spaces

This paper mainly studies the average sampling and reconstruction in shift-invariant subspaces of mixed Lebesgue spaces $L^{p,q}(\mathbb{R}^{d+1})$, under the condition that the generator $\varphi$ of the shift-invariant subspace belongs to a hybrid-norm space of mixed form, which is weaker than the usual assumption of Wiener amalgam space and allows to control the orders $p,q$. First, the sampling stability for two kinds of average sampling functionals are established. Then, we give the corresponding iterative approximation projection algorithms with exponential convergence for recovering the time-varying shift-invariant signals from the average samples.

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