EPFL | Biomedical Imaging Group | Exponential Wavelets

Exponential-Spline Wavelet Bases

I. Khalidov, M. Unser

Proceedings of the Thirtieth IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP'05), Philadelphia PA, USA, March 18-23, 2005, pp. IV-625–IV-628.

We build a multiresolution analysis based on shift-invariant exponential B-spline spaces. We construct the basis functions for these spaces and for their orthogonal complements. This yields a new family of wavelet-like basis functions of L₂, with some remarkable properties. The wavelets, which are characterized by a set of poles and zeros, have an explicit analytical form (exponential spline). They are nonstationary is the sense that they are scale-dependent and that they are not necessarily the dilates of one another. They behave like multi-scale versions of some underlying differential operator L; in particular, they are orthogonal to the exponentials that are in the null space of L. The corresponding wavelet transforms are implemented efficiently using an adaptation of Mallat's filterbank algorithm.

@INPROCEEDINGS(http://bigwww.epfl.ch/publications/khalidov0501.html,
AUTHOR="Khalidov, I. and Unser, M.",
TITLE="Exponential-Spline Wavelet Bases",
BOOKTITLE="Proceedings of the {IEEE} Thirtieth International Conference
	on Acoustics, Speech, and Signal Processing ({ICASSP'05})",
YEAR="2005",
editor="",
volume="{IV}",
series="",
pages="625--628",
address="Philadelphia PA, USA",
month="March 18-23,",
organization="",
publisher="",
note="")

© 2005 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.