Abstract
We mainly study the random sampling and reconstruction in multiply generated shift-invariant subspaces Vp,q(Φ) of mixed Lebesgue spaces Lp,q(R×Rd). Under suitable conditions for the generators Φ, 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 Vp,q(Φ) 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.
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