Average sampling and reconstruction for signals in shift‐invariant subspaces of weighted mixed Lebesgue spaces

2021 ◽  
Author(s):  
Suping Wang ◽  
Jiaxing Zhang
Keyword(s):  
Invariant Subspaces ◽  
Lebesgue Spaces ◽  
Average Sampling ◽  
Sampling And Reconstruction ◽  
Mixed Lebesgue Spaces

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.

scholarly journals Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces

2020 ◽  
Vol 18 (03) ◽  
pp. 2050013 ◽  
Author(s):  
Qingyue Zhang
Keyword(s):  
Invariant Subspaces ◽  
Reconstruction Algorithms ◽  
Lebesgue Spaces ◽  
Average Sampling ◽  
Sampling Problem ◽  
Fast Reconstruction ◽  
Mixed Lebesgue Spaces ◽  
Averaging Functions

In this paper, we study nonuniform average sampling problem in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. We discuss two types of average sampled values: average sampled values [Formula: see text] generated by single averaging function and average sampled values [Formula: see text] generated by multiple averaging functions. Two fast reconstruction algorithms for these two types of average sampled values are provided.

scholarly journals New Generalizations and Results in Shift-Invariant Subspaces of Mixed-Norm Lebesgue Spaces \({L_{\vec{p}}(\mathbb{R}^d)}\)

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 227 ◽  
Author(s):  
Junjian Zhao ◽  
Wei-Shih Du ◽  
Yasong Chen
Keyword(s):  
Invariant Subspace ◽  
Type Inequality ◽  
Invariant Subspaces ◽  
Minkowski Inequality ◽  
Hölder Inequality ◽  
Stability Theorem ◽  
Mixed Norm ◽  
Lebesgue Spaces

In this paper, we establish new generalizations and results in shift-invariant subspaces of mixed-norm Lebesgue spaces Lp→(Rd). We obtain a mixed-norm Hölder inequality, a mixed-norm Minkowski inequality, a mixed-norm convolution inequality, a convolution-Hölder type inequality and a stability theorem to mixed-norm case in the setting of shift-invariant subspace of Lp→(Rd). Our new results unify and refine the existing results in the literature.

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