Biomedical Imaging GroupSTI
English only   BIG > Publications > Summer School

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 PDF not available
 PS not available
 All BibTeX References

Sampling and Approximation Theory

M. Unser

Plenary talk, proceedings of the Summer School "New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis," Inzell, Federal Republic of Germany, September 17-21, 2007, pp. 15.

This tutorial will explain the modern, Hilbert-space approach for the discretization (sampling) and reconstruction (interpolation) of images (in two or higher dimensions). The emphasis will be on quality and optimality, which are important considerations for biomedical applications.

The main point in the modern formulation is that the signal model need not be bandlimited. In fact, it makes much better sense computationally to consider spline or wavelet-like representations that involve much shorter (e.g. compactly supported) basis functions that are shifted replicates of a single prototype (e.g., B-spline). We will show how Shannon's standard sampling paradigm can be adapted for dealing with such representations. In essence, this boils down to modifying the classical "anti-aliasing" prefilter so that it is optimally matched to the representation space (in practice, this can be accomplished by suitable digital post-filtering). Another important issue will be the assessment of interpolation quality and the identification of basis functions (and interpolators) that offer the best performance for a given computational budget.


AUTHOR="Unser, M.",
TITLE="Sampling and Approximation Theory",
BOOKTITLE="Summer School ``New Trends and Directions in Harmonic
        Analysis, Approximation Theory, and Image Analysis''",
address="Inzell, Federal Republic of Germany",
month="September 17-21,",
organization="{M}arie {C}urie Excellence Team {MAMEBIA} funded by the
        {E}uropean {C}ommission",
note="Plenary talk")

© 2007 . 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 .
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.