Multivariate Dynamical Sampling in $l^2({\mathbb{Z}}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

Abstract

In this paper, we investigate the multivariate dynamical sampling problem in $l^2({\mathbb{Z}}^2)$ associated with the two-dimensional discrete time non-separable linear canonical transform (2D-DT-NS-LCT) and shift-invariant spaces associated with the two-dimensional non-separable linear canonical transform (2D-NS-LCT), respectively. Specifically, we derive a sufficient and necessary condition under which a sequence in $l^2({\mathbb{Z}}^2)$ (or a function in a shift-invariant space) can be stably recovered from its dynamical sampling measurements associated with the 2D-DT-NS-LCT (or the 2D-NS-LCT). We also present a simple example to elucidate our main results.

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