U-Invariant Sampling and Reconstruction in Atomic Spaces With Multiple Generators

Given a U-invariant sampling scheme on a Hilbert space H. This paper characterizes atomic subspaces A of H such that every signal x ∈ A can be reconstructed from its generalized samples acquired with the U-invariant sampling scheme. If signal recovery is possible a linear filter is derived which reconstructs the signal from the samples. Moreover, the paper gives necessary and sufficient conditions on a sequence of sampling functions such that it forms a pseudoframe or pseudo-Riesz basis for a given atomic subspace A.