Biomedical Imaging GroupSTI
English only   BIG > Publications > Shifted Splines

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

Multiresolution Approximation Using Shifted Splines

F. Müller, P. Brigger, K. Illgner, M. Unser

IEEE Transactions on Signal Processing, vol. 46, no. 9, pp. 2555-2558, September 1998.

We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre- and post-filters as a function of the degree n and the shift parameter Δ. We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift-invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to the grid points (i.e., Δ=1/2 when n is odd, and Δ=0 when n is even). The worst case corresponds to the standard multiresolution setting where the spline spaces are nested.

AUTHOR="M{\"{u}}ller, F. and Brigger, P. and Illgner, K. and Unser,
TITLE="Multiresolution Approximation Using Shifted Splines",
JOURNAL="{IEEE} Transactions on Signal Processing",

© 1998 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.