Biomedical Imaging GroupSTI
English only   BIG > Publications > AR(1) Interpolation

 Home Page
 News & Events
 Tutorials and Reviews
 Download Algorithms

 All BibTeX References

Optimal Interpolation Laws for Stable AR(1) Processes

A. Amini, M. Unser

Proceedings of the Tenth International Workshop on Sampling Theory and Applications (SampTA'13), Bremen, Federal Republic of Germany, July 1-5, 2013, pp. 380-383.

In this paper, we focus on the problem of interpolating a continuous-time AR(1) process with stable innovations using minimum average error criterion. Stable innovations can be either Gaussian or non-Gaussian. In the former case, the optimality of the exponential splines is well understood. For non- Gaussian innovations, however, the problem has been all too often addressed through Monte Carlo methods. In this paper, based on a recent non-Gaussian stochastic framework, we revisit the AR(1) processes in the context of stable innovations and we derive explicit expressions for the optimal interpolator. We find that the interpolator depends on the stability index of the innovation and is linear for all stable laws, including the Gaussian case. We also show that the solution can be expressed in terms of exponential splines.

AUTHOR="Amini, A. and Unser, M.",
TITLE="Optimal Interpolation Laws for Stable {AR(1)} Processes",
BOOKTITLE="Proceedings of the Tenth International Workshop on Sampling
        Theory and Applications ({SampTA'13})",
address="Bremen, Federal Republic of Germany",
month="July 1-5,",

© 2013 SampTA. 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 SampTA.
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.