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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

Reconstruction algorithms in irregular sampling


Author: Karlheinz Gröchenig
Journal: Math. Comp. 59 (1992), 181-194
MSC: Primary 41A25; Secondary 41A80, 42A15, 65D99, 94A12
MathSciNet review: 1134729
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Abstract: A constructive solution of the irregular sampling problem for band-limited functions is given. We show how a band-limited function can be completely reconstructed from any random sampling set whose density is higher than the Nyquist rate, and give precise estimates for the speed of convergence of this iteration method. Variations of this algorithm allow for irregular sampling with derivatives, reconstruction of band-limited functions from local averages, and irregular sampling of multivariate band-limited functions.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1992-1134729-0
PII: S 0025-5718(1992)1134729-0
Keywords: Band-limited functions, irregular sampling, Wirtinger's inequality
Article copyright: © Copyright 1992 American Mathematical Society