Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The -Theory

Author(s): Akram Aldroubi; Hans Feichtinger
Journal: Proc. Amer. Math. Soc. 126 (1998), 2677-2686.
MSC (1991): Primary 42C15, 46A35, 46E15, 46N99, 47B37
MathSciNet review: 1451788
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Abstract: We prove that the exact reconstruction of a function from its samples on any ``sufficiently dense" sampling set $\{x_i\}_{i\in \Lambda}$ can be obtained, as long as is known to belong to a large class of spline-like spaces in $L^p(\cal R^n)$ . 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.

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