Multivariate Dynamical Sampling in 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 (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 $l^2({\mathbb{Z}}^2)$ (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.

Keywords:

• Linear canonical transform (LCT)
• multivariate dynamical sampling
• shift-invariant spaces

MOS SUBJECT CLASSIFICATION::

• 94A20
• 94A12
• 42C15
• 43A32

Additional information

Funding

This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 11801256 and 12061044).