  In this paper, we discuss to the nonuniform sampling problem in principal
shift-invariant subspaces of mixed Lebesgue spaces. We proposed a fast
reconstruction algorithm which allows to exactly reconstruct the functions in
the principal shift-invariant subspaces as long as the sampling set
$X=\{(x_{j},y_{k}):k,j\in \mathbb{J}\}$ is sufficiently dense. Our results
improve the result in \cite{LiLiu}.
