We mainly study the random sampling and reconstruction in multiply generated shift-invariant subspaces $V^{p,q}\left(\Phi \right)$ of mixed Lebesgue spaces $L^{p,q}(\mathbb{R}\times {\mathbb{R}}^d)$. Under suitable conditions for the generators $\Phi$, we can prove that if the sampling sizes are large enough for both variables, the sampling stability holds with high probability for all functions in $V^{p,q}\left(\Phi \right)$ whose energy is concentrated on a compact subset. Finally, a reconstruction algorithm based on random samples is given for functions in a finite dimensional subspace.

中文翻译：

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混合Lebesgue空间的多重生成的移不变子空间中的随机采样 ${\mathrm{大号}}^{p，q}（\mathbb{[R}\times {\mathbb{[R}}^d）$

我们主要研究多重生成的移位不变子空间中的随机采样和重构 $V^{p，q}（\Phi ）$ Lebesgue空间的混合 ${\mathrm{大号}}^{p，q}（\mathbb{[R}\times {\mathbb{[R}}^d）$。在适合发电机的条件下$\Phi$，我们可以证明，如果两个变量的样本量都足够大，则对于 $V^{p，q}（\Phi ）$其能量集中在一个紧凑的子集上。最后，针对有限维子空间中的函数，给出了基于随机样本的重构算法。