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Mathematics of Computation

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Reconstruction algorithms in irregular sampling
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by Karlheinz Gröchenig PDF
Math. Comp. 59 (1992), 181-194 Request permission

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
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 181-194
  • MSC: Primary 41A25; Secondary 41A80, 42A15, 65D99, 94A12
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1134729-0
  • MathSciNet review: 1134729