EPFL | Biomedical Imaging Group

Sampling: Beyond the Myth of a Perfect Reconstruction

M. Unser

Plenary talk, Proceedings of the Fourth International Conference on Sampling Theory and Applications (SampTA'01), Orlando FL, USA, May 13-17, 2001, pp. 15.

The key idea that we want to convey in this talk is that the principle of a perfect reconstruction in sampling is too strong a constraint; it requires mathematical assumptions on the class of input signals and measurement systems that are rarely met in practice. Instead, we should consider a more realistic form of the problem where the goal is to get the best approximation possible from the signal measurements given a chosen set of basis functions (model), or, alternatively, some reconstruction device. We will develop this idea in the special case of uniform sampling, presenting research results on the approximation of functions in "shift-invariant" spaces, including splines and wavelets. Practically, this allows for simpler—and possibly more realistic—interpolation models, which can be used in conjunction with a much wider class of (anti-aliasing) pre-filters that are not necessarily ideal lowpass. We will summarize and discuss the results available for the determination of the approximation error and of the minimum sampling rate when the input of the system is essentially arbitrary; e.g., non-bandlimited. Finally, we will review some variations of sampling that can be understood from the same unifying perspective. These include wavelets, multi-wavelets, Papoulis generalized sampling, finite elements, and frames.

For more details and bibliography, we refer to M. Unser, "Sampling—50 Years After Shannon," Proceedings of the IEEE, vol. 88, no. 4, pp. 569-587, April 2000.

See also the tutorials and reviews.

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser0101.html,
AUTHOR="Unser, M.",
TITLE="Sampling: {B}eyond the Myth of a Perfect Reconstruction",
BOOKTITLE="Proceedings of the Fourth International Conference on
	Sampling Theory and Applications ({SampTA'01})",
YEAR="2001",
editor="",
volume="",
series="",
pages="15",
address="Orlando FL, USA",
month="May 13-17,",
organization="",
publisher="",
note="Plenary talk")

© 2001 SampTA. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from SampTA. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.