EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Shift-Orthogonal Wavelets


 CONTENTS
 Home Page
 News & Events
 People
 Publications
 Tutorials and Reviews
 Research
 Demos
 Download Algorithms

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Construction of Shift-Orthogonal Wavelets Using Splines

M. Unser, P. Thévenaz, A. Aldroubi

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing IV, Denver CO, USA, August 6-9, 1996, vol. 2825, part I, pp. 465-473.



We present examples of a new type of wavelet basis function that are orthogonal across shifts, but not across scales. The analysis functions are low order splines (piecewise constant or linear) while the synthesis functions are polynomial splines of higher degree n2. The approximation power of these representations is essentially as good as that of the corresponding Battle-Lemarié orthogonal wavelet transform, with the difference that the present wavelet synthesis filters have a much faster decay. This last property, together with the fact that these transformations are almost orthogonal, may be useful for image coding and data compression.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser9606.html,
AUTHOR="Unser, M. and Th{\'{e}}venaz, P. and Aldroubi, A.",
TITLE="Construction of Shift-Orthogonal Wavelets Using Splines",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical
        Imaging: {W}avelet Applications in Signal and Image Processing
        {IV}",
YEAR="1996",
editor="",
volume="2825",
series="",
pages="465--473",
address="Denver CO, USA",
month="August 6-9,",
organization="",
publisher="",
note="{Part {I}}")

© 1996 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.