EPFL
 Biomedical Imaging GroupSTI
EPFL
  Publications
English only   BIG > Publications > Fast Continuous Wavelet


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

 DOWNLOAD
 PDF
 Postscript
 All BibTeX References

Fast Continuous Wavelet Transform: A Least-Squares Formulation

M.J. Vrhel, C. Lee, M. Unser

Signal Processing, vol. 57, no. 2, pp. 103-119, March 1997.



We introduce a general framework for the efficient computation of the real continuous wavelet transform (CWT) using a filter bank. The method allows arbitrary sampling along the scale axis, and achieves O(N) complexity per scale where N is the length of the signal. Previous algorithms that calculated non-dyadic samples along the scale axis had O(Nlog(N)) computations per scale. Our approach approximates the analysing wavelet by its orthogonal projection (least-squares solution) onto a space defined by a compactly supported scaling function. We discuss the theory which uses a duality principle and recursive digital filtering for rapid calculation of the CWT. We derive error bounds on the wavelet approximation and show how to obtain any desired level of accuracy through the use of longer filters. Finally, we present examples of implementation for real symmetric and anti-symmetric wavelets.


@ARTICLE(http://bigwww.epfl.ch/publications/vrhel9702.html,
AUTHOR="Vrhel, M.J. and Lee, C. and Unser, M.",
TITLE="Fast Continuous Wavelet Transform: {A} Least-Squares
        Formulation",
JOURNAL="Signal Processing",
YEAR="1997",
volume="57",
number="2",
pages="103--119",
month="March",
note="")

© 1997 Elsevier. 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 Elsevier.
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.