Dynamical sampling in ℓ2(Z)(d) and vector shift-invariant spaces

Abstract

Dynamical sampling problem in which we seek to reconstruct a sequence or function in evolutionary systems via spatiotemporal trade-off. In this paper, we present the problem of dynamical sampling in ℓ²(Z)^(d) and vector shift-invariant spaces. We first give a sufficient and necessary condition under which c∈ℓ²(Z^d)^(d) can be recovered by its spatial and temporal samples. Then to illustrate our main result, we give two examples to show that the sufficient and necessary condition in the main result is feasible. Finally, we study the dynamical sampling problem in vector shift-invariant spaces.