Biomedical Imaging GroupSTI
English only   BIG > Publications > Hermite Splines

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 PDF not available
 PS not available
 All BibTeX References

Statistical Optimality of Hermite Splines for the Reconstruction of Self-Similar Signals

V. Uhlmann

SIAM Conference on Imaging Science (SIS'18), Bologna, Italian Republic, June 5-8, 2018, session MS47-2.

Hermite splines are commonly used for interpolating data when samples of the derivative are available, in a scheme called Hermite interpolation. Assuming a suitable statistical model, we demonstrate that this method is optimal for reconstructing random signals in Papoulis' generalized sampling framework. More precisely, we show the equivalence between cubic Hermite interpolation and the linear minimum mean-square error (LMMSE) estimation of a second-order Lévy process.

AUTHOR="Uhlmann, V.",
TITLE="Statistical Optimality of {H}ermite Splines for the
        Reconstruction of Self-Similar Signals",
BOOKTITLE="{SIAM} Conference on Imaging Science ({SIS'18})",
address="Bologna, Italian Republic",
month="June 5-8,",
note="session MS47-2")

© 2018 SIAM. 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 SIAM.
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.