Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Exact iterative reconstruction algorithm for multivariate irregularly sampled functions in spline-like spaces: The $L^p$-theory

Authors: Akram Aldroubi and Hans Feichtinger
Journal: Proc. Amer. Math. Soc. 126 (1998), 2677-2686
MSC (1991): Primary 42C15, 46A35, 46E15, 46N99, 47B37
MathSciNet review: 1451788
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 42C15, 46A35, 46E15, 46N99, 47B37

Retrieve articles in all journals with MSC (1991): 42C15, 46A35, 46E15, 46N99, 47B37

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

Hans Feichtinger
Affiliation: University of Vienna, Department of Mathematics, Strudlhofg. 4, A-1090 Wien, Austria
MR Author ID: 65680
ORCID: 0000-0002-9927-0742

Keywords: Non-uniform sampling, shift-invariant spaces, Riesz basis
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.
Dedicated: Dedicated to the memory of Richard J. Duffin
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1998 American Mathematical Society