Reconstruction algorithms in irregular sampling

Author:
Karlheinz Gröchenig

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

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-1992-1134729-0

Keywords:
Band-limited functions,
irregular sampling,
Wirtinger's inequality

Article copyright:
© Copyright 1992
American Mathematical Society