Biomedical Imaging GroupSTI
English only   BIG > Publications > MOMS

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

MOMS: Maximal-Order Interpolation of Minimal Support

T. Blu, P. Thévenaz, M. Unser

IEEE Transactions on Image Processing, vol. 10, no. 7, pp. 1069-1080, July 2001.

We consider the problem of interpolating a signal using a linear combination of shifted versions of a compactly-supported basis function φ(x). We first give the expression of the φ's that have minimal support for a given accuracy (also known as "approximation order"). This class of functions, which we call maximal-order-minimal-support functions (MOMS), is made of linear combinations of the B-spline of same order and of its derivatives.

We provide the explicit form of the MOMS that maximize the approximation accuracy when the step-size is small enough. We compute the sampling gain obtained by using these optimal basis functions over the splines of same order. We show that it is already substantial for small orders and that it further increases with the approximation order L. When L is large, this sampling gain becomes linear; more specifically, its exact asymptotic expression is (2 L ⁄ (π × e)). Since the optimal functions are continuous, but not differentiable, for even orders, and even only piecewise continuous for odd orders, our result implies that regularity has little to do with approximating performance.

These theoretical findings are corroborated by experimental evidence that involves compounded rotations of images.

AUTHOR="Blu, T. and Th{\'{e}}venaz, P. and Unser, M.",
TITLE="{MOMS}: {M}aximal-Order Interpolation of Minimal Support",
JOURNAL="{IEEE} Transactions on Image Processing",

© 2001 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.