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

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