Multivariate Dynamical Sampling in and Shift-Invariant Spaces Associated with Linear Canonical Transform. (23rd May 2022) - Huo, Haiye; Xiao, Li
Abstract: In this paper, we investigate the multivariate dynamical sampling problem in l 2 ( Z 2 ) associated with the two-dimensional discrete time non-separable linear canonical transform (2 D-DT-NS-LCT) and shift-invariant spaces associated with the two-dimensional non-separable linear canonical transform (2 D-NS-LCT), respectively. Specifically, we derive a sufficient and necessary condition under which a sequence in l 2 ( Z 2 ) (or a function in a shift-invariant space) can be stably recovered from its dynamical sampling measurements associated with the 2 D-DT-NS-LCT (or the 2 D-NS-LCT). We also present a simple example to elucidate our main results.