Exact Reconstruction of Spatially Undersampled Signals in Evolutionary Systems

We consider the problem of spatiotemporal sampling in which an initial state f of an evolution process ft = Atf is to be recovered from a combined set of coarse samples from varying time levels {t1, . . . , tN}. This new way of sampling, which we call dynamical sampling, differs from standard sampling since at any fixed time ti there are not enough samples to recover the function f or the state fti . Although dynamical sampling is an inverse problem, it differs from the typical inverse problems in which f is to be recovered from AT f for a single time T . In this paper, we consider signals that are modeled by `(Z) or a shift invariant space V ⊂ L(R).