Multivariate Dynamical Sampling in ℓ2(ℤd) and Shift-Invariant Spaces

Zhang, Qingyue; Li, Zunxian

doi:10.1080/01630563.2018.1561471

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2021

2022

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“…However, all the mentioned dynamical sampling results above focus on onedimensional signals. Motivated by applications in multi-dimensional signal systems, Zhang et al [31] considered the multivariate dynamical sampling in l 2 (Z d ) and shift-invariant spaces associated with the d-dimensional FT.…”

Section: Introductionmentioning

confidence: 99%

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

Huo¹,

Xiao²

2021

Preprint

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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 (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 (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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Section: Introductionmentioning

confidence: 99%