LAUSR

Abstract In this paper, we study the nonuniform sampling and reconstruction problem in shift-invariant subspaces of mixed Lebesgue spaces. We first show that shift-invariant subspaces in mixed Lebesgue spaces L p , q ( R d + 1 ) can be well-defined. Then we propose that the sampling problem in shift-invariant subspaces of mixed Lebesgue spaces is well-posed. At last, the nonuniform samples { f ( x j , y k ) : k , j ∈ J } of a function f belonging to a shift-invariant subspace of mixed Lebesgue spaces are proposed, and we give a fast reconstruction algorithm that allows exact reconstruction of f as long as the sampling set X = { ( x j , y k ) : k , j ∈ J } is sufficiently dense.