EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Karhunen-Loève Transform


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

 DOWNLOAD
 PDF not available
 PS not available
 All BibTeX References

An Extension of the Karhunen-Loève Transform for Wavelets and Perfect Reconstruction Filterbanks

M. Unser

Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet Applications in Signal and Image Processing, San Diego CA, USA, July 15-16, 1993, vol. 2034, pp. 45-56.



Most orthogonal signal decompositions, including block transforms, wavelet transforms, wavelet packets, and perfect reconstruction filterbanks in general, can be represented by a paraunitary system matrix. The author considers the general problem of finding the optimal P × P paraunitary transform that minimizes the approximation error when a signal is reconstructed from a reduced number of components Q < P. This constitutes a direct extension of the Karhunen-Loève transform which provides the optimal solution for block transforms (unitary system matrix). General solutions are presented for the optimal representation of arbitrary wide sense stationary processes. The author also investigates a variety of suboptimal schemes using FIR filterbanks. In particular, it is shown that low-order Daubechies wavelets and wavelet packets (D2 and D3) are near optimal for the representation of Markov-1 processes.


@INPROCEEDINGS(http://bigwww.epfl.ch/publications/unser9309.html,
AUTHOR="Unser, M.",
TITLE="An Extension of the {K}arhunen-{L}o{\`{e}}ve Transform for
        Wavelets and Perfect Reconstruction Filterbanks",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical
        Imaging: {W}avelet Applications in Signal and Image Processing",
YEAR="1993",
editor="",
volume="2034",
series="",
pages="45--56",
address="San Diego CA, USA",
month="July 15-16,",
organization="",
publisher="",
note="")

© 1993 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.