Journal of Computational and Applied Mathematics ( IF 2.037 ) Pub Date : 2020-10-08 , DOI: 10.1016/j.cam.2020.113237
Yingchun Jiang; Wan Li

We mainly study the random sampling and reconstruction in multiply generated shift-invariant subspaces ${V}^{p,q}\left(\Phi \right)$ of mixed Lebesgue spaces ${L}^{p,q}\left(\mathbb{R}×{\mathbb{R}}^{d}\right)$. 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.

down
wechat
bug