Multivariate Dynamical Sampling in and Shift-Invariant Spaces Associated with Linear Canonical Transform. (23rd May 2022)

• Record Type: Journal Article
• Authors: Huo, Haiye; Xiao, Li
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 5(2022)
• Page Start: 541
• Page End: 557
• Publication Date: 2022-05-23
• Subjects: Linear canonical transform (LCT) -- multivariate dynamical sampling -- shift-invariant spaces; 94A20 -- 94A12 -- 42C15 -- 43A32; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2051185
• Languages: English
• ISSNs: 0163-0563

Abstract

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.