Biomedical Imaging GroupSTI
English only   BIG > Publications > Relaxing Compact Support

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

Why Restrict Ourselves to Compactly Supported Basis Functions?

M. Unser, T. Blu

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing IX, San Diego CA, USA, July 29-August 1, 2001, vol. 4478, pp. 311-314.

Compact support is undoubtedly one of the wavelet properties that is given the greatest weight both in theory and applications. It is usually believed to be essential for two main reasons: (1) to have fast numerical algorithms, and (2) to have good time or space localization properties. Here, we argue that this constraint is unnecessarily restrictive and that fast algorithms and good localization can also be achieved with non-compactly supported basis functions. By dropping the compact support requirement, one gains in flexibility. This opens up new perspectives such as fractional wavelets whose key parameters (order, regularity, etc…) are tunable in a continuous fashion. To make our point, we draw an analogy with the closely related task of image interpolation. This is an area where it was believed until very recently that interpolators should be designed to be compactly supported for best results. Today, there is compelling evidence that non-compactly supported interpolators (such as splines, and others) provide the best cost/performance tradeoff.

AUTHOR="Unser, M. and Blu, T.",
TITLE="Why Restrict Ourselves to Compactly Supported Basis
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical
        Imaging: {W}avelet Applications in Signal and Image Processing
address="San Diego CA, USA",
month="July 29-August 1,",

© 2001 SPIE. 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 SPIE.
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.