Biomedical Imaging GroupSTI
English only   BIG > Publications > Quantitative L2

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

Quantitative L2 Error Analysis for Interpolation Methods and Wavelet Expansions

T. Blu, M. Unser

Proceedings of the 1997 IEEE International Conference on Image Processing (ICIP'97), Santa Barbara CA, USA, October 26-29, 1997, vol. I, pp. 663-666.

Our goal in this paper is to set a theoretical basis for the comparison of re-sampling and interpolation methods. We consider the general problem of the approximation of an arbitrary continuously-defined function f(x)—not necessarily bandlimited—when we vary the sampling step T. We present an accurate L2 computation of the induced approximation error as a function of T for a general class of linear approximation operators including interpolation and other kinds of projectors. This new quantitative result provides exact expressions for the asymptotic development of the error as T→0, and also sharp (asymptotically exact) upper bounds.

AUTHOR="Blu, T. and Unser, M.",
TITLE="Quantitative {$L^{2}$} Error Analysis for Interpolation
        Methods and Wavelet Expansions",
BOOKTITLE="Proceedings of the 1997 {IEEE} International Conference
        on Image Processing ({ICIP'97})",
address="Santa Barbara CA, USA",
month="October 26-29,",

© 1997 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.