Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The $L^p$-theory
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- by Akram Aldroubi and Hans Feichtinger PDF
- Proc. Amer. Math. Soc. 126 (1998), 2677-2686 Request permission
Abstract:
We prove that the exact reconstruction of a function $s$ from its samples $s (x_i)$ on any “sufficiently dense" sampling set $\{x_i\}_{i\in \Lambda }$ can be obtained, as long as $s$ is known to belong to a large class of spline-like spaces in $L^p (\mathcal {R}^n)$. Moreover, the reconstruction can be implemented using fast algorithms. Since a limiting case is the space of bandlimited functions, our result generalizes the classical Shannon-Whittaker sampling theorem on regular sampling and the Paley-Wiener theorem on non-uniform sampling.References
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Additional Information
- Akram Aldroubi
- Affiliation: National Institutes of Health, Biomedical Engineering and Instrumentation Program, Bethesda, Maryland 20892
- Address at time of publication: Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240
- Email: aldroubi@helix.nih.gov, aldroubi@math.vanderbilt.edu
- Hans Feichtinger
- Affiliation: University of Vienna, Department of Mathematics, Strudlhofg. 4, A-1090 Wien, Austria
- MR Author ID: 65680
- ORCID: 0000-0002-9927-0742
- Email: fei@tyche.mat.univie.ac.at
- Received by editor(s): January 28, 1997
- Additional Notes: This research was partially supported through the FWF-project S-7001-MAT of the Austrian Science Foundation.
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 126 (1998), 2677-2686
- MSC (1991): Primary 42C15, 46A35, 46E15, 46N99, 47B37
- DOI: https://doi.org/10.1090/S0002-9939-98-04319-6
- MathSciNet review: 1451788
Dedicated: Dedicated to the memory of Richard J. Duffin