TY - JOUR
T1 - An L2-stability estimate for periodic nonuniform sampling in higher dimensions
AU - Frederick, Christina
N1 - Funding Information:
This work has benefited from valuable discussions and insights from Bjorn Engquist, Kasso Okoudjou, David Walnut, Haomin Zhou, and an anonymous reviewer. This research was supported in part by NSF grants OISE-1317015 , DMS-1720306 , and Institut Mittag-Leffler .
Funding Information:
This work has benefited from valuable discussions and insights from Bjorn Engquist, Kasso Okoudjou, David Walnut, Haomin Zhou, and an anonymous reviewer. This research was supported in part by NSF grants OISE-1317015, DMS-1720306, and Institut Mittag-Leffler.
Publisher Copyright:
© 2018
PY - 2018/10/15
Y1 - 2018/10/15
N2 - 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.
AB - 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.
KW - Inverse Vandermonde matrices
KW - Periodic nonuniform sampling
KW - Stable sampling
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U2 - 10.1016/j.laa.2018.06.014
DO - 10.1016/j.laa.2018.06.014
M3 - Article
AN - SCOPUS:85049310491
SN - 0024-3795
VL - 555
SP - 361
EP - 372
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
ER -