Biomedical Imaging GroupSTI
English only   BIG > Publications > Fractional Splines

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

The Fractional Spline Wavelet Transform: Definition and Implementation

T. Blu, M. Unser

Proceedings of the Twenty-Fifth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'00), Istanbul, Turkey, June 5-9, 2000, vol. I, pp. 512-515.

We define a new wavelet transform that is based on a recently defined family of scaling functions: the fractional B-splines. The interest of this family is that they interpolate between the integer degrees of polynomial B-splines and that they allow a fractional order of approximation.

The orthogonal fractional spline wavelets essentially behave as a fractional differentiators. This property seems promising for the analysis of 1/fα; noise that can be whitened by an appropriate choice of the degree of the spline transform.

We present a practical FFT-based algorithm for the implementation of these fractional wavelet transforms, and give some examples of processing.

AUTHOR="Blu, T. and Unser, M.",
TITLE="The Fractional Spline Wavelet Transform: {D}efinition and
BOOKTITLE="Proceedings of the Twenty-Fifth {IEEE} International
        Conference on Acoustics, Speech, and Signal Processing
address="Istanbul, Turkey",
month="June 5-9,",

© 2000 IEEE. 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 IEEE.
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.