An L2-stability estimate for periodic nonuniform sampling in higher dimensions

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Abstract

We consider sampling strategies for a class of multivariate bandlimited functions f that have a spectrum consisting of disjoint frequency bands. Taking advantage of the special spectral structure, we provide formulas relating f to the samples f(y),y∈X, where X is a periodic nonuniform sampling set. In this case, we show that the reconstruction can be viewed as an iterative process involving certain Vandermonde matrices, resulting in a link between the invertibility of these matrices to the existence of certain sampling sets that guarantee a unique recovery. Furthermore, estimates of inverse Vandermonde matrices are used to provide explicit L2-stability estimates for the reconstruction of this class of functions.

Original languageEnglish (US)
Pages (from-to)361-372
Number of pages12
JournalLinear Algebra and Its Applications
Volume555
DOIs
StatePublished - Oct 15 2018

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics

Keywords

  • Inverse Vandermonde matrices
  • Periodic nonuniform sampling
  • Stable sampling

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